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UNITED STATES OF AMERICA. 



GRAVITATION THE DETERMINING 
FORCE. 



GRAVITATION 
THE DETERMINING FORCE 



/ 



ETHAN SAMUEL CHAPIN, A. M. 



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X 




CAMBRIDGE 

JMnteD at tije ftitarstoe $m£ 

1887 



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Copyright, 1887, 
By ETHAN SAMUEL CHAPIN. 

Ml rights reserved. 



The Riverside Fresa, Cambridge : 
Electrotyped and Printed by H. 0. Houghton & Co. 



As 

A TOKEN OF PARENTAL LOV^, 

E Srttcatc tfjese $ageg 

TO 

MY DAUGHTER, 

WHO HAS BEEN MY COMPANION AND HELPER 

IN THEIR PREPARATION, 

AMID THE INCESSANT CARES OF A 

DISTRACTING- BUSINESS. 



NOTE. 

For assistance in the preparation of this 
revised edition, reading of proofs, and the 
general supervision of the work of publication, 
I am indebted to the Rev. M. C. Stebbins, 
A. M., formerly of this city, and now of 
Cornwall, Vt. 

E. S. CHAPIN. 

Springfield, Mass. 
September, 1887. 



PKEFACE. 



In 1864 I presented to the public a pam- 
phlet entitled " Gravity and Heat." Three 
years later I published a duodecimo volume of 
120 pages, entitled " Gravitation in Nature." 
In these publications were set forth some con- 
clusions which I had reached, as the result of 
reflection and experiment prosecuted during 
such brief intervals as I could command in 
the midst of the pressing cares of business. 
The study had not only given me real pleas- 
ure, but had driven me to conclusions that 
were certainly important if true. The clear- 
ness and firmness of my convictions seemed 
to me a justification of their publication, al- 
though my conclusions were at variance, in 
many points, with the current opinions of 
standard authors, and of the public who fol- 
lowed them. 

It has been to me the occasion of special 
satisfaction, that several of our most thorough 
and eminent students of physical science, as 



X PREFACE. 

the result of their latest research and experi- 
ment, have reached conclusions in substantial 
accord with mine. This is especially notice- 
able in regard to the following topics : The 
physical condition of Jupiter ; The incon- 
stancy of the Earth's rotation upon its axis 
as set forth by Father Secchi of Rome and 
quoted by Professor Newcomb ; Gravitation 
the source of heat, etc. 

This recent and authoritative confirmation 
of conclusions to which I was logically driven 
more than twenty years ago has seemed to me 
a sufficient reason for revising and reprinting 
this unpretending volume, under the title, 
" Gravity the Determining Force." 

ETHAN SAMUEL CHAPIN. 

Springfield, Mass., 1887. 



CONTENTS. 



CHAPTER I. 

GRAVITY CAUSES INCREASE OF DENSITY, HIGHER TEMPERA- 
TURE, AND FLUIDITY OF MATTER. 

Variations of density dependent upon variations of grav- 
ity. — The expansive tendency of heat resisted by 
gravity. — Density and conductivity of matter de- 
pend upon position and condition. — Conductivity 
varies with density. — Interdependence of tempera- 
ture, density, compressibility, and resistance. — Con- 
traction affected by pressure. — Bearing of the pre- 
ceding laws upon the condition of the earth. — 
Sustaining strength of the crust of the earth. — Thick- 
ness of the earth's crust only approximately deter- 
mined. — Tendency of heat toward the centre of the 
earth. — A fused nucleus. — Objections to the theory 
of a fused nucleus. — Conclusions of William Hop- 
kins, F. E,. S. — The surface of the earth changed 
from fluid to solid by influence of gravity. — Ap- 
parent exceptions to law of increasing density. — 
Effect of contraction upon condition and dimensions 
of the earth. — Elevations and depressions, how pro- 
duced. — Superficial changes now going on. — Up- 
heavals and depressions, how caused. — Causes of 
fracture. — Changes in coast line. — Mountains, 
glaciers, moraines. — Location of progressive subsi- 



di CONTENTS. 

dences. — Origin, cause, and location of current dis- 
turbances in the earth's crust. — Subsidence and up- 
lifting reciprocal. — Uplifting and leveling forces 
kept in equilibrium. — Where leveling forces are 
most active. — Sustaining strength of the earth's crust 
limited. — Causes modifying disturbance resulting 
from fracture. — Conditions under which earthquakes 
are specially liable to occur. — Varying distances, 
centrifugal and centripetal forces. — Volcanic vents. 

— The earth's crust thin, and the interior hot. — 
Possible transitions of heat and matter. — Heat and 
gravity correlative. — Relation of gravity to cohesion. 

— Effect of the removal of gravity. — Consequence 
of the restoration of gravity. — Process of refrigera- 
tion. — Equalization of temperature. — Direction and 
form of inequalities, how determined. — Ocean cur- 
rents modified by earth's motion. — Inequality of 
temperature a cause of springs 

Sections I.-XLIII. pp. 1-62 



CHAPTER II. 

THE THEORY OF THE TIDES. 

Influence of sun and moon upon the tides, as presented 
by different writers. — Causes assigned inadequate to 
produce the effect. — Relative force of different ele- 
ments. — Influence of the earth's rotation. — Result- 
ant of the several elements. — Reciprocal motions of 
earth and moon. — Instability of the earth's axis, and 
its effect. — Result were the position of the earth's 
axis invariable. — Cause of axial rotation. — Projec- 
tile from a rifled gun. — Exceptions to Herschel's 
view. — A complex problem. — Forces considered, 
adequate to produce the tides. — Location of high 
tides Sections XLIV.-LVII. pp. G3-85 



CONTENTS. Xlll 

CHAPTER III. 

PRECESSION, NUTATION, AND OBLIQUITY OF THE ECLIPTIC. 

Precession. — Newton's theory. — Influence of redun- 
dant matter at the earth's equator. — Fallacy of the 
Newtonian hypothesis. — Real causes of precession. 
— Causes of precession illustrated. — Amount of 
annual precession variable. — Maximum and minimum 
eccentricity. — Herschel on the stability of the earth's 
axis. — Variable direction of the influence of disturb- 
ing bodies. — Axis of rotation not coincident with the 

geometrical axis. — Theories of nutation 

Sections LVIII.-LXVTII. pp. 86-99 

CHAPTER IV. 

THE SECULAR ACCELERATION OF THE MOON'S MEAN 
MOTION. 

Moon's acceleration. — Hypothesis of Laplace. — Objec- 
tions to the hypothesis of Laplace. — Is the earth's 
orbit becoming a circle ? — Moon's acceleration not 
due to change in orbit. — Moon's acceleration not due 
to ethereal resistance. — Laplace traces the cause of 
lunar acceleration to the sun. — Influence of the sun 
and moon on the stability of the earth's axis. — The 
sun's motion an element in the problem. — The lunar 
acceleration likely to continue indefinitely .... 

Sections LXIX.-LXXVIIL pp. 100-111 

CHAPTER V. 

GRAVITATION IN THE SOLAR SYSTEM. 

Laws of matter uniform throughout the solar system. — 
Forces that determine the moon's path. — Unequal 
density of the superior and inferior limbs of the moon, 
and of comets. — Illustrative experiments. — The 



iv CONTENTS. 

rarer limb moves in the longer orbit. — The balanced 
condition of the moon and other satellites. — Condi- 
tions likely to affect the temperature of the moon's 
surface. — Laws determining magnitude of melted 
nucleus. — Varying density of the planets. — Spots 
and faculas on the sun's surface. — The sun not de- 
teriorating. — Thickness of crust of the earth, Jupiter, 
and of the moon. — Location of the greatest inequali- 
ties. — Motion of the line of the apsides. — Exterior 
and interior condition of Jupiter. — Condition of the 
planetary envelopes. — Geological and meteorological 
phenomena upon Jupiter and Saturn. — Heat radiated 
from the earth does not pass the limits of the atmos- 
phere .... Sections LXXIX.-XCVI. pp. 112-141 



CHAPTER VI. 

PRINCIPLES OF PLANETARY MOTION, AND ETHEREAL 
RESISTANCE. 

Theories of resistance to planetary motion. — The ring 
hypothesis of Laplace. — Facts inconsistent with the 
ring hypothesis. — Axial rotation not explained by 
the ring hypothesis. — Significance of recent dis- 
coveries, etc. — Initial effects of gravitation. — Be- 
ginning of orbital motion. — Composition of forces. — 
Discoveries of Newton and Kepler. — Question of in- 
terplanetary resistance undecided. — Important re- 
sults of experiment, and their practical application. 
— The distances and periodic times of planets and 
comets indicate the absence of a resisting medium. — 
Author's conclusions harmonize with Scriptural repre- 
sentations. — Space originally pervaded by homo- 
geneous nebulous matter. — The consummation . . 

Sections XCVII.-CXI. pp. 142-169 



GKAVITATION THE DETERMINING 
FORCE. 



CHAPTER I. 

GRAVITY CAUSES INCREASE OF DENSITY, 
HIGHER TEMPERATURE, AND FLUIDITY 
OF MATTER. 



Variations* of Density Dependent upon Va- 
riations oe Gravity. 

If molten matter be congealed while under 
pressure, the density of the congealed mass 
will be greater than if the congelation had 
taken place while the matter was free from 
such pressure. The greater the pressure, the 
greater the resulting density, until a limit is 
reached beyond which the density will be 
nearly or quite uniform. Now, as the force 
of terrestrial gravitation decreases as the 
square of the distance from the earth's center 
increases, it follows that its condensing power 
is less on the mountain heights than at the 



2 GRAVITATION 

level of the sea ; and less at the equator than 
at distances nearer either pole. All the tests 
that we can apply combine to prove : That 
the force of gravitation determines the den- 
sity of matter, 

II. 

The Expansive Tendency of Heat Kesisted 
by Geavity. 

The expansive force of heat opposes the 
condensing tendency of gravitation, as is seen 
in the expansion of matter when the tempera- 
ture is raised. But the expansion of a fluid 
mass resulting from an increase of tempera- 
ture is less in proportion as it is subjected to 
greater pressure. For example, if we apply 
heat to a vessel of water in a receiver from 
which a considerable portion of the air has 
been removed, we shall see how much more 
readily it yields to the expansive force, and at 
how much lower temperature it will be con- 
verted into steam. Hence we conclude : That 
the expansive power of heat is limited by the 
force of gravitation and the elasticity of the 
matter heated. 



THE DETERMINING FORCE. 



m. 

Density and Conductivity of Matter Depend 
upon Position and Condition. 

In the "Principia," Book II. Prop. 20, 
Newton maintains that any single particle of 
a spherical fluid mass is pressed toward its 
center by the force of its own gravity, but if 
a second particle rests upon the first, the pres- 
sure is doubled ; a third particle will make 
the pressure treble ; a fourth, quadruple, and 
so on. 

This law of Newton respecting pressure, 
like the laws given in some of our text-books 
to explain the expansion and contraction re- 
sulting from an increase or diminution of 
temperature, is only applicable to matter in 
certain positions. Let the earth be the spher- 
ical mass to which the law is applied, and sup- 
pose the first particle to be located on the 
earth's surface at its mean distance from the 
center, as on the 45th degree of latitude ; a 
second particle placed above this would prac- 
tically double the pressure, but as we go on 
building up particle upon particle, it is evident 
that the law, in order to be accurate, must 
take account of the decrease of gravitation 



4 GRAVITATION 

with the increase of distance from the center. 
The expansion and contraction with, or with- 
out, a variation of temperature, contrary to 
the laws given in the tables of many of our 
text-books, vary with the pressure. Since the 
above was first written, the principle here laid 
down has been repeatedly demonstrated by 
striking practical experiments. In the " Sci- 
entific American " for January 1, 1876, under 
the heading, " Expansion and Contraction by 
Change of Temperature under great Strain," 
we find the following : " It is well known 
that metals expand or contract by the rise or 
descent of temperature, according to co-effi- 
cients found by careful experiments, and laid 
clown in the books; but it appears that the 
amount of this effect of heat and cold can 
only be correctly determined beforehand in 
cases where the metals are under no great 
strain of extension or expansion. . . . This 
has been forcibly illustrated in the case of the 
great steel bridge in St. Louis, Mo., with its 
arches of 500 feet span. Calculations and 
allowances were made for expansion and con- 
traction by heat and cold through a range of 
140° Fall., and the difference to be expected 
in the elevation of the center arch of the 
upper chord, above the City Directrix, from 



THE DETERMINING FORCE. 5 

the hottest clay of summer to the coldest day 
of winter, was calculated to be about 18 
inches. . . . The result of almost daily ob- 
servations ranging through 106° of tempera- 
ture showed an actual difference in height of 
8A inches. The difference for this range of 
temperature, according to the tables, should 
have been about 14 inches. But we observe 
that, in the case of the Victoria Bridge at 
Montreal, the expansion in summer and con- 
traction in winter is in perfect accord with the 
calculation; in this bridge, however, the ex- 
pansion is only longitudinal, and is not coun- 
teracted by any strain ; while in the case of the 
St. Louis bridge the expansion has to overcome 
the immense strain exerted by the weight of 
the structure itself and the load upon the arch, 
... so that for an arch with slight elevation 
in the center, the strain becomes very great, 
and often surpasses the actual weight many 
times. . . . 

" In the case of the Suspension Bridge at 
Niagara, it was found that the elevation by 
contraction was less than the calculation gave 
ground to expect ; here, too, the material acts 
under an immense strain." 

The effect of an increase or diminution of 
pressure upon expansion and contraction may 



6 GRAVITATION 

not be perceptible in bodies of small mass, but 
could be very readily detected in a body of 
such magnitude as that of the earth. With- 
out attempting to determine the amount of 
the variation in pressure, density, expansion, 
or contraction due to the superposition of 
matter at different altitudes, I conclude : That 
the density of matter, in all its forms, de- 
pends on the force of gravitation and the 
weight of particle on particle. The expan- 
sive force of heat must be taken into account 
in this connection. 

If we take a tube a few feet in length, 
closed at both ends, fill it with molten matter 
while the tube is in a horizontal position, close 
the aperture, and then raise one end till the 
tube is vertical, the molten matter will no 
longer fill it, because the increased pressure 
has increased the density of the fluid mass. 
If the matter contained in the tube were not 
heated, its density would not be sensibly af- 
fected by the change of position and slight 
increase of pressure. This experiment shows, 
That the expansive force of heat is more 
readily overcome ivhen matter is molten, and 
that the density of matter depends, in a meas- 
ure, on the pressure of particle on particle ; for 
by placing the tube of molten matter in a verti- 



THE DETERMINING FORCE. 7 

cal position, gravitation acts less on the mat- 
ter ; for, as a whole, it is removed farther from 
the center of the earth, but the pressure and 
density are greater. 

rv. 

Conductivity Yaeies with Density. 

When the density of matter is uniform, its 
conducting power is also uniform ; but if we 
pulverize a solid body, or in any way increase 
or diminish the density of a body, we increase 
or reduce its conducting power. It is evident 
then, That the conductivity of matter in- 
creases ivith the density. 

If we apply condensing force to a mass of 
liquid matter, such force affects equally every 
portion of the entire mass. But if the liquid 
mass have considerable depth, its density can- 
not be uniform, since the density of the lower 
portion would be increased by the weight of 
the upper. 

If we apply heat to homogeneous matter of 
uniform density, the conducting power tends 
to diffuse the heat equally through the mass ; 
if the density is not uniform the denser por- 
tion will receive the larger measure of heat, 
since the conductivity of the successive strata 
tends to convey the heat from the rarer to the 
denser part. 



GRAVITATION 



Interdependence of Temperature, Density, 
Compressibility, and Besistance. 

If we compress a cubic foot of air, or of 
other matter, into a smaller space than it pre- 
viously occupied, it will, henceforth, be less 
easily compressed. The general result may 
therefore be thus stated: The capacity of 
matter to sustain a crushing force increases 
with the density. As heat, the equivalent of 
force, is made apparent by resistance, the 
temperature of matter is increased by com- 
pression, as all substances indicate. It has 
been said that if a mixture of ice and water 
be compressed the temperature of the mixture 
will be lowered. This may seem to be an 
exception to the above law, but we should 
remember that the formation of ice affords a 
partial exception to the law that cold con- 
tracts all bodies, since the greatest density is 
reached above the freezing point. It is evi- 
dent, too, that a portion of the heat resulting 
from compression is utilized in melting the 
ice. 

Solid substances are more easily compressed 
when their temperature has been raised. The 



THE DETERMINING FORCE. 9 

compressibility of congealed matter, there- 
fore, increases with the temperature. 



VI. 

Contraction Affected by Pressure. 

Fused matter, as a rule, under ordinary at- 
mospheric pressure contracts one eighth of an 
inch per foot in congealing. If the pressure 
is lessened before and during the process of 
congelation, the resultant density will be di- 
minished, but the amount of contraction will 
be increased. But if the pressure be aug- 
mented before and during the process of con- 
gelation, the resultant contraction will be less 
than one eighth of an inch per foot, the ex- 
pansive force of heat having yielded to the 
pressure before congelation took place. Hence 
we deduce the proposition : The amount of 
contraction in matter, consequent upon re- 
frigeration, depends, in a measure, upon its 
density. 

VII. 

Bearing of the Preceding Laws upon the 
Condition of the Earth. 

By the application of the preceding laws 
we are led to the conclusion that as we go 



10 GRAVITATION 

down toward the center of the earth we must 
reach a level where matter ceases to contract 
by pressure, or to expand by heat. Compres- 
sion increases the density of matter, but as 
the ultimate molecules are supposed to be in- 
compressible, the distance between them must 
decrease,. until the expansive force of heat is 
overcome, and the molecules are forced into 
contact by the superincumbent mass, caus- 
ing what may be termed perfectly condensed 
matter ; and as heat is the equivalent of the 
intense force resisted, this matter must be 
intensely hot. Some scientists maintain that 
no amount of pressure could bring the ulti- 
mate molecules into actual contact. Were 
this to be conceded, our conclusion would not 
be affected, since under the condition supposed 
all known forces tending to keep the mole- 
cules asunder have given way to pressure. 



vni. 

Sustaining Strength of the Crust of the 
Earth. 

Many experiments have been tried to deter- 
mine the sustaining strength of the various 
rocks of which the crust of the earth is com- 
posed ; but experiments have not been suffi- 



THE DETERMINING FORCE. \\ 

ciently extended upon matter varying in den- 
sity and temperature, like the earth's crust, 
to furnish data for a definite estimate of the 
height to which a column of such matter could 
be built up before its base would be crushed. 
The height of the column would vary with its 
position on the earth's surface ; for the weight 
of matter increases as we approach the poles, 
and decreases as we go toward the equator, 
or ascend a mountain. If we suppose the 
column to have been congealed from a molten 
state, its height would vary with the locality, 
since its density would depend, in a measure, 
upon the varying force of gravitation at these 
different places. If the column were cast in 
a vertical position in the earth, it would in- 
crease in density toward the center of the 
earth : the increase in density would add to 
its sustaining strength ; but as there is more 
or less heat in the surface stratum, the tem- 
perature must be increasing with the density 
as we descend, and the sustaining strength 
would decrease as the temperature became 
very high. 



12 GRAVITATION 



IX. 



Thickness of the Earth's Crust only Ap- 
proximately Determined. 

Further experiments may be necessary to 
determine, or approximate very nearly, the 
distance below the surface of the earth where 
a stratum would be crushed by the superin- 
cumbent mass. This stratum, at whatever 
depth it is located, is the boundary between 
the rigid crust and the fluid interior of the 
earth. Since the density, conducting power, 
and temperature increase as we descend in the 
earth, and the sustaining strength decreases 
as the temperature rises, it is probable that 
this boundary between the solid crust and the 
fluid interior is comparatively near the sur- 
face. It has been shown that matter in- 
creases in density as the pressure to which it 
is subjected increases; but this increase of 
density may not continue to any very oreat 
depth, for, if it did, the earth would be much 
heavier than it is estimated to be. We may 
suppose the earth's crust to be made up of an 
infinite number of columns all pointing 
toward the earth's center ; the variation in the 
length of these columns would represent the 



THE DETERMINING FORCE. 13 

thickness of the crust in their several local- 
ities. 

The combined surface of the exterior bases 
of these columns would make up the surface 
of the earth, while the combined surface of 
their bases toward the earth's center would 
make up the boundary surface of the fluid 
sphere, or melted nucleus. That we should 
have the melted nucleus is evident ; for when 
the base of the solid column is crushed, the 
resistance to the intense force is great, and the 
crushed portion must be intensely hot, even 
to fluidity. As each column of which the 
earth's crust is supposed to be made up is 
perfectly wedged in by the columns around 
it, the crushed portions of one could not es- 
cape in a lateral direction, for the surround- 
ing matter on the same level would also be 
crushed, and must therefore be equally hot 
and equally dense. If we should attempt to 
lengthen the shaft by adding matter to the 
exterior base, the interior base would be 
crushed. If we should remove a portion of 
the superincumbent weight from the exterior 
base, the heat would expand a portion of the 
matter of the crushed interior base ; the in- 
tense fluid heat, the equivalent of the crush- 
ing force, would disappear, and the matter 



14 GRAVITATION 

would be refrigerated. Hence we see that the 
length of the column would not be increased 
or diminished by overloading or lightening 
its exterior base. 



Tendency of Heat toward the Center of 
the Earth. 

Heat being the equivalent of the force re- 
sisted tends toward the earth's center, not 
only by the force of compression, but this 
tendency is also favored by conduction, for 
heat inclines toward the denser strata which, 
if undisturbed, underlie the rarer. Both these 
causes favor the concentration of heat in the 
deeper regions of the earth. Although heat 
is being constantly conveyed from the central 
portions to the surface, by thermal springs, 
volcanoes, and other similar agencies ; and be- 
yond the surface by the shifting currents of 
the atmosphere, it is not lost, as it is being 
constantly conducted back toward the center 
of the earth by the increasing density, and 
the consequent greater conductivity of the 
strata in that direction. The prevailing di- 
rection of the currents indicates that they are 
tending to produce an equalization of tem- 
perature; as a general rule, therefore, they 
move in opposition to conduction. 



THE DETERMINING FORCE. 15 

That heat tends to accumulate in the cen- 
tral portions of the earth may be confirmed 
still further by observations upon a tube of 
molten matter, such as we noted in Section 
III. We found that, by changing it from 
the horizontal to the vertical position, the 
bulk of the molten mass was diminished, but 
its quantity of heat remains undiminished ; 
therefore it contains more heat per cubic foot 
than before. We shall also note an accumu- 
lation of heat in the lower portion, caused 
both by the increase of density and by the 
consequent increase of conductivity in that 
direction. 

Again : for an additional confirmation of 
the tendency of heat to concentrate in the 
interior portions of the earth, let us exam- 
ine different strata in a vertical column of 
sand. We find that as we descend from stra- 
tum to stratum, there is a perceptible in- 
crease in the number of grains per cubic inch, 
as well as an increase of sustaining strength ; 
we must, therefore, admit that there is a cor- 
responding increase of force, the equivalent of 
heat. If we cast a molten shaft in a vertical 
position, the conditions being such that all 
portions may be refrigerated as nearly as pos- 
sible at the same instant, we shall find, as we 



16 GRAVITATION 

test the shaft from the top downward, an in- 
crease of density, and of crushing force ; we 
shall also find an increase of conducting 
power, and a consequent increase of heat in 
the same direction. Now, let us suppose that 
our refrigerated shaft is one of the infinite 
number of columns that make up the solid 
crust of the earth, as in Section IX. If we 
could apply our tests to it in this position, 
we should find the same continual increase of 
crushing force, density, conducting power, and 
heat, as far as we could go ; and as these prop- 
erties increase in matter, according to the 
pressure, we must infer that the same law of 
increase holds good for the depths that are 
beyond our penetration. 



XI. 

A Fused Nucleus. 
Could we penetrate these depths we should 
find a melted nucleus which must be more 
dense than the crust, for a solid will not be 
supported by a fluid of less specific gravity 
than itself. It would sink, as ice on a lake 
would sink, if it should be overloaded ; and if 
the solid crust were subject to a compressing 
force equal to that which acts on the melted 



THE DETERMINING FORCE. 17 

nucleus, it would itself be crushed, and be 
made fluid by the condensation. The crust 
rests on partially fused matter, and that on the 
melted nucleus, and heat is not conducted 
from the nucleus to the surface, since matter 
decreases in density and conducting power 
in that direction. As the crust has been dis- 
turbed, the decrease in density is not regular ; 
but the conductivity of the strata decreases 
very regularly, owing to the interjection of 
comparatively rare matter, in veins, dikes, and 
fissures, at the times of the various disturb- 
ances. 

xn. 

Objections to the Theory of a Fused 
Nucleus. 

The theory of a melted nucleus seems to 
be discarded by many scientists. The " Amer- 
ican Encyclopaedia " says: "It is controverted 
by Sir Charles Lyell, M. Poisson, and other 
eminent authorities, on these grounds. When 
substances, as metals, are melted, their tem- 
perature cannot be raised a single degree 
above the point of fusion, so long as a piece 
of the material remains unmelted. The same 
principle is exemplified in the impossibility of 
raising water to a higher temperature than 



18 GRAVITATION 

32 F., so long as a fragment of ice remains 
in it." 

These objections to a melted nucleus may 
at first seem unanswerable, but they vanish 
before thoughtful investigation. When a 
portion of matter on the surface of the earth 
is melted, the melted portion is usually rarer 
than the remaining solid part, and if the two 
remain in contact, the solid portion must be 
melted, provided that there is sufficient heat, 
as heat is naturally conveyed from the rarer 
to the denser portion. Solids that neither ex- 
pand by fusion nor contract by refrigeration, 
have the same density whether in the fluid or 
solid state, and owing to the tendency of heat 
to diffuse itself equally the solid and fluid 
parts soon come to be of equal temperature 
when they are brought together. If the fused 
portion of any substance were denser than the 
remaining solid portion, the latter would take 
a superior position when they were brought 
together ; but the temperature of each would 
approach as near that of the other as does the 
density of inferior and superior strata of little 
thickness. Under such conditions, it may be 
said that the whole mass must be fused, or 
the whole be congealed, for there would be 
no appreciable difference of temperature be- 



THE DETERMINING FORCE. 19 

tween the opposite surfaces of a stratum of so 
little thickness.; but a descent of from fifty 
to sixty feet gives us a difference of a degree 
of temperature, if we leave out of account the 
varying surface influences. Water, unlike 
solid substances in general, expands when it 
congeals ; the line of transition between the 
solid and fluid is definite and sharply drawn, 
although the variation of the thermometer in 
passing from one to the other may not be 
perceptible. The water is denser and warmer 
than the particles of ice that rest upon it. Let 
us suppose a mass of ice composed of several 
horizontal strata, the lowest stratum being the 
densest, and each one above it rarer than the 
one upon which it rests ; then the lowest 
would have the largest measure of cohesive 
and resisting force, the equivalent of heat ; 
the cohesive and resisting force would ptow 
less and less from the lowest to the upper- 
most stratum, and the temperature would fol- 
low the same law. Like the water, the melted 
nucleus is denser and hotter than the crust 
that rests upon it, but as the variation of tem- 
perature — unlike the case of the water and 
ice — is considerable, between what may be 
termed solid and fluid, so the distance in the 
earth is considerable, between perfect fluidity 



20 GRAVITATION 

and the solid crust, comprising some miles of 
thickening matter, until we arrive at congealed 
matter, or a crust twenty miles, more or less, 
in thickness. 

XIII. 
Conclusions of William Hopkins, F. K. S. 

From the results of experiments upon sev- 
eral different kinds of rock, William Hopkins, 
F. R. S., of London, concluded that the density 
and conducting power of the inferior strata 
greatly exceed those of the superior, and 
hence inferred that the melted nucleus must 
be hundreds of miles from the surface. The 
temperature of the surface strata is variable ; 
but if, lower down, the density and conduct- 
ing power of the crust were uniform, the tem- 
perature would be uniform also. In this 
case, an inferior stratum at a great depth 
would have the same temperature as a stra- 
tum near the surface. But as the density of 
the different strata increases with the pres- 
sure to which they are severally subjected, 
and their conducting power increases with the 
density, the nucleus must be intensely hot. 

The more rapidly the conducting power in- 
creases as we descend, the nearer the surface 
of the earth should we find the surface of the 



THE DETERMINING FORCE. 21 

fluid nucleus. In a paper read in 1860 be- 
fore the Royal Institution, London, by Wil- 
liam Hopkins, F. R. S., be gives some of tbe 
cod elusions that he had reached as the result 
of investigations to ascertain how far the 
observed amount of precession might be con- 
sistent with the existence of a fluid nucleus, 
and among them is this : " In assuming the 
recognized period of precession, the shell in 
question, in order that it promote such a re- 
sult, must be at least one fifth of the earth's 
radius in thickness." The reasonableness of 
this conclusion will be considered in a subse- 
quent chapter. 

XIV. 

The Surface of the Earth Changed from 
Fluid to Solid by Influence of Gravity. 

As the density of matter depends on the 
force of gravitation, matter must have existed 
prior to its condensation by gravitation. And 
as resistance increases with the increase of 
density, the matter of which the earth is com- 
posed must have been made hot by condensa- 
tion. There must have been a time, therefore, 
when the earth ivas in a molten condition. 

Ever since the creation, gravitation has 
been producing its effects on the earth, and 



22 GRAVITATION 

has by its powerful and all pervading influ- 
ence increased the density of matter ; but this 
increase of density has been unequal in 
different portions of the earth in consequence 
of the pressure of superior upon inferior 
masses, hence we have as a necessary result 
that the central portions of the earth are the 
more dense. Heat, being more readily con- 
ducted by the denser matter, receded from the 
surface, producing gradual refrigeration, and 
ultimately a solid crust : the same causes that 
produced this crust would continue to increase 
its thickness until the refrigeration had 
reached a depth at which its effects are over- 
come by pressure, and heat ceases to recede. 
With the density and conducting power of 
the different strata as they are, the present 
thickness of the solid crust is about what we 
ought to expect, if we suppose it to have been 
in a fluid state at creation. 



XV. 

Apparent Exceptions to Law of Increasing 
Density. 

A large portion of the crust became rigid 
while under greater pressure than it is sub- 
jected to in the position which it now occu- 



THE DETERMINING FORCE. 23 

pies, and dissimilar rock and strata vary more 
or less in density and power of transmitting 
heat, when formed under equal pressure. 
These disturbances and variations cause the 
thermometer to indicate different degrees of 
temperature in different localities at the same 
depth. If the rock underlying any point was 
formed originally near the surface, and then 
caused to subside by the superincumbent mass, 
but without sufficient weight to crush it, its 
density and temperature might not be greater 
than those of the strata a little distance above ; 
or, if rock rests upon a stratum of gravel and 
bowlders, conditions that may be seen in the 
Alps; or, if the conducting power of the in- 
ferior stratum be less than that of the supe- 
rior, we should naturally have an exception 
to the law that temperature increases with the 
depth. This may account for occasional in- 
stances that are cited to disprove the univer- 
sality of the law. 

XVI. 

Effect of Contraction upon Condition and 
Dimensions of the Eaeth. 

Conduction has caused the heat of fluidity 
that was originally distributed through the 
matter which is now the solid crust to recede 



K 



24 GRAVITATION 

to the interior and denser portions. The re- 
frigeration and contraction of the surface 
took place first, that being the least dense : 
the inferior strata, being refrigerated subse- 
quently, caused a lateral pressure on the sur- 
face stratum, proportionate to the contraction 
of the inferior strata, or the extra surface due 
to the heights and depressions on the surface 
of the earth. 

If we suppose the crust to be twenty or 
thirty miles, more or less, in thickness, and to 
have contracted in congealing as much as iron 
or granite would do under similar conditions, 
which would be about one eighth of an inch 
per linear foot on the surface of the earth, 
and much less at the depth where the crust 
meets the fluid nucleus, as there the expansive 
force of heat would be largely overcome by 
pressure, we should then have a medium con- 
traction of the crust of about one sixteenth 
of an inch per linear foot. Hence, it appears 
that our globe would have been but a few 
thousand feet larger in diameter, when in a 
fluid state, than it now is. It may seem that 
a crust only twenty or thirty miles in thick- 
ness would be too thin and weak, but ice a 
foot in thickness resting upon the surface of 
water will sustain many tons ; were it a few 



THE DETERMINING FORCE- 25 

rods in thickness, it would readily support 
large buildings. 

xvn. 

Elevations and Depressions, How Pro- 
duced. 

As the refrigeration of the inferior strata 
advanced, the heavier portions of the solid 
crust gained a mechanical advantage over the 
lighter. This augmented by the lateral pres- 
sure on the surface stratum caused the eleva- 
tion of mountains and the depression of 
valleys. As the force of gravity on elevated 
matter decreases inversely as the square of 
the distance from the center of the earth, 
the table-lands and mountains, as they were 
uplifted, became ' self-sustaining. As the 
weight of portions of the crust was diminished, 
by their elevation, so, by the breaking up of 
the uniform sphericity, the weight was un- 
equally distributed and the sustaining strength 
was weakened. A part of the weight of the 
mountains and table-lands, being thrown upon 
the valleys and depressed portions, caused 
great changes in the solid strata. 



26 GRAVITATION 

xvin. 

Superficial Changes now going on. 

The superficial changes which are now tak- 
ing place are comparatively trifling, — local 
rather than general, — and are produced 
mostly by the aqueous agents that are chang- 
ing the position of matter, and disturbing the 
equilibrium of the crust. But the tendencies 
of nature to level the surface of the earth, 
through aqueous and other agencies, are coun- 
terbalanced; for the removal of matter from 
the surf ice in any locality allows as much 
matter to expand at the opposite base resting 
on the fluid nucleus, as is caused to contract 
in another portion of the crust over the fluid 
nucleus by the deposit of an additional mass 
upon the surface above it. When any por- 
tion of the crust is loaded beyond its sustain- 
ing strength, it is crushed by the force of 
gravity on the superincumbent mass, and 
made fluid by resistance ; while an equal 
amount of the matter of the fused nucleus 
rises with those portions that are. becoming 
lighter, above the line of fluidity. When the 
pressure is diminished, the melted matter ex- 
pands, the heat of fluidity disappears, and 



THE DETERMINING FORCE. 27 

uniformity of pressure, density, and tempera- 
ture is gradually restored to every portion in 
contact with the fluid stratum. That the 
matter of the fused nucleus expands before 
congelation takes place to form the rock strata, 
seems very evident ; for, if the granite or 
rock strata had been formed at the depth of 
many miles, it would have been necessary for 
them to withstand the immense pressure of 
the overlying mass, and in that case would 
have been able to sustain an equal pressure in 
their elevated position ; indeed, they would 
have had even greater power to resist pres- 
sure, because of their diminished temperature. 
But such is not the fact. Again, if we take 
any representative rock that is admitted to 
have belonged to the lower strata, we find 
that its specific gravity is only about one half 
the average specific gravity of the earth's en- 
tire mass. This seems conclusive evidence 
that the matter of the fused nucleus must ex- 
pand before refrigeration takes place to form 
the comparatively light rock strata of the 
earth's crust. 



28 GRAVITATION 



XIX. 

Upheavals and Depressions, How Caused. 

The crust varies in thickness in different 
localities, as would the length of the column 
necessary to produce the conditions that result 
in the status of the fluid nucleus. The varia- 
tion of the centrifugal force in different por- 
tions of the earth, affects the density and 
thickness of the crust only as it affects grav- 
ity. Centrifugal force counteracts the force 
of gravitation in a greater or less degree, 
according to latitude. The thickness of the 
crust increases as we approach the equator, 
since in that locality the force of gravitation is 
less on account of the spheroidal figure of the 
earth. The crust where the surface is at the 
average distance from the center is of medium 
thickness, and the more elevated portions 
show an increase of thickness proportionate 
to their elevation. When we consider, first, 
how much shorter is the vertical line that 
measures the thickness of the crust than is 
the circumference either of its outer or its 
inner surface, and, secondly, that the direction 
of the disturbing forces is mainly vertical, it 
becomes evident that we must look for up- 



THE DETERMINING FORCE. 29 

heavals and depressions as the result of the 
action of these disturbing forces, and as we 
can determine the localities where surface 
changes are most active, we can determine 
where the crust is most liable to undergo 
fracture. 

If matter is removed from any locality on 
the surface of the earth, the melted nucleus 
recedes from that locality. If matter be 
added to any portion of the surface, the nu- 
cleus moves toward that portion. The ap- 
proach of the fluid nucleus to any point is 
equivalent to the subsidence of that point ; 
and the recession of the nucleus from any 
point is equivalent to its upheaval, when com- 
pared with the level of the sea ; for while the 
melted nucleus conforms to the center of 
pressure, the level of the sea also conforms to 
that center. Neither the altitude of moun- 
tains, nor their number, taken as a whole, is 
being reduced by the leveling forces. 

XX. 

Causes of Fkacture. 

When large deposits of matter are being 
made in any locality, that locality is subsid- 
ing ; while the district from which the matter 



30 GRAVITATION 

is being removed is rising ; this double move- 
ment brings a longitudinal strain upon the 
rising section, and at the same time a lateral 
pressure upon that which is sinking. The 
resistance of rock strata to a crushing force 
far exceeds its ability to resist tension. The 
lateral tension to which the strata of the crust 
are subjected renders them liable to fracture 
near the summit of the portions that are being 
uplifted. But the portions subject to the 
greatest lateral strain are those that lie nearly 
equidistant between the line of greatest up- 
heaval and the line of greatest depression ; 
they are therefore most liable to such frac- 
tures as allow the melted nucleus to be forced 
up to the surface, and sometimes to form vol- 
canoes. The line of fracture is usually near 
the level of the sea, and is generally identical 
with the line of faults. 



XXI. 

Changes in Coast Line. 

When large deposits of foreign matter are 
being made near the coast, that portion of the 
continent is subsiding. If the district from 
which material is being removed lies contigu- 
ous to a sea or an ocean, that sea or ocean is 



THE DETERMINING FORCE. 31 

retiring. Thus, in one locality, the sea is en- 
croaching on the land, and in another, the 
land is encroaching on the sea, as, alternately, 
the solid crust is being depressed to form the 
bed of an ocean, or raised to form a mountain 
summit. If we could change our field of ob- 
servation from the outer to the interior surface 
of the crust, we should there see in one local- 
ity the strata of the solid crust, whether ig- 
neous or aqueous, being transformed by con- 
densation from the solid to the fluid state ; 
while in another, because the pressure had 
been diminished, we should see a portion of 
the melted nucleus expanding, its heat of flu- 
idity disappearing, and thus, by refrigeration, 
new plutonic rock being formed. 

This rock, formed underneath localities 
where the crust had been lightened, and sub- 
sequently thrown up by ■ disturbing forces in 
the course of ages, by the action of leveling 
agencies, is laid bare on the summit of some 
high mountain, and in its turn furnishes ma- 
terial for aqueous strata ; for its disintegrated 
particles are carried down by every mountain 
stream, and deposited on river and ocean beds, 
where, by compression, they are brought under 
the influence of cohesion, and solidified into 
stratified rock. 



32 GRAVITATION 



XXII. 

Mountains, Glaciers, Moraines. 
^ The older mountains are not always the 
higher, for large deposits of foreign material 
near their bases may have caused their gradual 
subsidence. The plutonic rock is, therefore, 
found at all levels, between the ocean and the 
summit of the lofty and more recently formed 
mountains. The position of the organic re- 
mains found in stratified rocks makes it evi- 
dent that these rocks have some time formed 
the bed of the ocean, while the glacial furrows 
which they bear clearly indicate that they, as 
well as the plutonic rocks, have some time been 
above the line of perpetual frost, and have 
been ground down and defaced by the weight 
and force of moving glaciers. It has been 
shown that the elevated and the depressed por- 
tions of the earth are continually changing 
their positions. Mountains with glaciers mov- 
ing down their slopes have undoubtedly ex- 
isted in every latitude on the surface of the 
earth. Rocks found in different localities, but 
having a marked resemblance to each other, 
and which, for this reason, are said to belong 
to particular epochs, were doubtless formed 



THE DETERMINING FORCE. 33 

by similar agencies, but in very different ages 
of the world. The same may be said of gla- 
cial furrows, which were grooved when the 
rocks which bear them rested at altitudes 
quite different from their present. Similarity 
of appearance and structure in rocks is not 
evidence that they have equal, or any definite 
age, although some geologists have fixed upon 
a particular period of the past and styled 
it " the glacial and drift epoch" and have 
sought to make a chronological catalogue of 
the rocks. The energy and extent of glacial 
and drift action are not diminished as time 
advances, and may never have been greater, 
in the aggregate, than now. 

Glaciers are transporting moraines and 
grooving the rocks as in former days. Ice- 
bergs and flowing ice are smoothing and stri- 
ating rocks ; are scattering bowlders, gravel, 
and drift on the floor of the ocean, as they 
did in past ages, when the present continents 
formed the bed of the ocean. As the motion 
of ocean currents, with their fields of floating 
ice often touching the bed of the ocean, is 
from the poles toward the equator, the striae 
which they are producing, as well as the 
bowlders and drift which they are conveying, 
are strewed in a northerly and southerly di- 



34 GRAVITATION- 

rection. Of this, abundant evidence may be 
found all over the surface of North America 
and in other portions of the globe. 

The uplifting of the crust from the level of 
the ocean to the line of perpetual frost, with 
the consequent changes in the currents of the 
ocean, gives to the same locality, in the course 
of years, a radical change of climate. 

XXIII. 

Location of Pkogressive Subsidences. 

Since the earth as a whole has ceased to 
contract, these changes may have become less 
rapid ; but, in many localities, the lapse of a 
few centuries makes them easily discernible. 
The subsidence may be seen near the places 
where large deposits of material are being 
made, as at the estuaries of some rivers ; there 
trees are found in a growing posture, buried 
below the level of the sea ; and sometimes the 
sinking of the land has submerged large 
buildings. 

On those portions of a continent which are- 
subsiding, the promontories and mountains are 
becoming islands ; while other mountains com- 
posed of various strata are being formed on 
those portions which are losing matter and are 



THE DETERMINING FORCE. 35 

being uplifted. This uplifting of the land 
from the ocean bed is most apparent where 
extended high lands or mountain ranges are 
near one side of the continent, and run ap- 
proximately parallel to the water line, as is the 
case on the western coast of South America. 
Other conditions being equal, these changes 
of level are the most rapid where the surface 
inequalities are most marked, as is the case in 
the warmer climates. Where many forces 
have combined to change the level of a par- 
ticular locality with unusual rapidity, some 
implements of the aborigines have become 
buried to a considerable depth, causing un- 
warranted skepticism in the minds of a few 
eminent men, regarding the reliability of the 
Mosaic account of the age of man on the 
earth. 

The effects of upheaval and depression are, 
in various ways, permanently preserved in the 
solid crust, by fractures, dislocation, etc. A 
fracture that was produced in the surface stra- 
tum at, or near, the summit of an uplift, is 
usually represented by a rent ; a like force 
acting upon the hotter and more plastic strata 
underlying the same locality, would produce 
a fold. Before the faults were disturbed they 
were probably on a line near the level of the 



36 GRAVITATION 

ocean. If erosion and denudation were very 
unequal on opposite sides of the continent, 
they may represent a somewhat greater alti- 
tude. As volcanoes are formed on those lines 
where the changes of level are the most fre- 
quent, and where the crust is subjected to the 
greatest lateral strain, they are found more or 
less in belts. 

XXIV. 

Origin, Cause, and Location of Current 
Disturbances in the Earth's Crust. 

My purpose does not lead me to an extended 
description of the geographical, or the geologi- 
cal features of the earth ; to note minutely 
the variations of temperature as we descend 
through the crust ; or to name the localities 
of the most frequent changes, and of the 
most violent disturbances. This ground has 
been covered with considerable care and 
thoroughness by writers upon physical geog- 
raphy, and by scientists who have made the 
phenomena of earthquakes and the distribu- 
tion of volcanoes a special study. I propose 
to confine myself to the origin and cause 
of these conditions and disturbances, and to 
indicate the portion of the crust, the condi- 
tions of the elements, and the seasons of the 



THE DETERMINING FORCE. 37 

year, in which they are most likely to occur. 
As the currents of seas and oceans, with their 
denudating and transporting forces, are sub- 
ject to more frequent fluctuations than are 
inland streams; islands, peninsulas, and prom- 
ontories are more liable to experience up- 
heaval and depression than are portions of the 
mainland. The peninsula of Italy affords a 
striking illustration of this. 

Writers on physical geography have sug- 
gested that inland tropical seas, which, with 
no visible outlet, are receiving a constant in- 
flux of salt, may be filling up, since none of 
the salt that is brought in is carried away by 
the active evaporation that is constantly re- 
moving the water from the surface. But 
even if the tendency to the accumulation of 
salt were not counteracted, as Lieut. Maury 
suggests, in his " Physical Geography of the 
Sea," by the tireless industry of the number- 
less legions of coral insects and similar tenants 
of the deep ; and if all the excess of salt should 
be deposited on the bottom of the sea, it would 
not follow that the capacity of the sea is being 
diminished : for it has been shown that any 
extended portions of land, sea, or ocean which 
are receiving large deposits of matter, whether 
salt, coral, or any other substance, are for the 



38 GRAVITATION 

time subsiding. To this law, however, there 
may be exceptions. A locality may be up- 
lifted, though it is receiving some deposits of 
foreign matter, provided it be situated nearly 
equidistant between two localities each of 
which is subsiding under the weight of an ex- 
cess of deposit. In such a case the upheaval 
would result naturally from the subsidence 
of the more heavily weighted district on each 
side. This may account for the uplifting of 
some of the coral islands in the central por- 
tion of the Pacific Ocean. 

Here and there a limited section may be 
found that is being uplifted, even while it is 
receiving deposits: because it belongs to a 
district which, as a whole, is being lightened. 
Illustrations of this are seen in some valleys ; 
in lake and volcanic regions. Lakes thus 
situated are gradually filling up, — Lake 
Geneva is an example. Instances of an oppo- 
site character are occasionally found ; a lim- 
ited section that is being lightened may be 
undergoing a depression of level, because it 
belongs to a more extended district, which, as 
a whole, is being overloaded and is conse- 
quently going down. Some islands, penin- 
sulas, capes, and promontories apparently come - 
under this case. 



THE DETERMINING FORCE. 39 

XXV. 

Subsidence and Uplifting Reciprocal. 

The subsidence of the heavier portions of 
the crust and the uplifting of the lighter are 
like the effect that would be produced on an 
arch constructed of slightly elastic material if 
the equilibrium of the arch should be dis- 
turbed by lightening one part of its span and 
overloading another. The weighted part 
would sink, causing the Lighter part to rise. 
It is evident that there would be a tendency 
of the uplifted portions to remain supported 
in their elevated positions, since by being 
elevated they would lose something of their 
weight, and a part would be transferred to the 
more depressed portions of the crust. That 
sections of the crust are being uplifted, and 
that something of their weight rests on the 
adjacent valleys, is evident from the frequent 
land-slides. If this were not true, such phe- 
nomena as land-slides would be unknown, and 
banks of earth and gravel with perpendicular 
sides would be familiar sights. 

Let Fig. 1 represent a mountain supported 
in part by its base extending below the level 
of the sea, and in part by the lateral pressure 




Fig. 1. 



40 GRAVITATION 

of the adjacent portions below the same level. 
Let represent the level of an ocean on one 
side, and P an extended plain on the opposite 
side ; 1, 4, 7, 9 wonld represent the extended 
and submerged base. 
If the sides of this 
mountain, instead of be- 
ing sloping, were verti- 
cal, making the upper 
base equal to the lower, 
the lower part might be 
crushed by the excessive weight above it. 

In the Yosemite Valley we have an instance 
in point. The complicated fracture of the 
rock disengaged a column with sides nearly 
perpendicular ; its diameter seven or eight, 
and its circumference about twenty-five miles. 
In this disengaged column the weight of the 
superincumbent mass exceeded the sustaining 
strength of the base ; the base was crushed ; 
the mass sunk down hundreds of feet, and 
would have gone down still further had not 
the descent been arrested by the lateral pres- 
sure of the crust against the expanded base. 






THE DETERMINING FORCE. 41 



XXVI. 

Uplifting and Leveling Forces Kept in 
Equilibrium. 

As the crust is supported on the melted 
nucleus and the inequalities on the surface 
poise each other, great mountain chains must 
he balanced by a deep sea, or by a large ex- 
tent of low level plain. The established facts 
of astronomy indicate that the diameter of the 
earth is practically invariable, therefore the 
elevations must, in the aggregate, equal the 
depressions. These movements of upheaval 
and subsidence counterbalance the levering 
forces and maintain an equilibrium of the in- 
equalities on the surface of the earth. Had 
not this been the case, it is evident from the 
thickness of the various strata of rock that, 
during the protracted geological periods which 
are admitted to have intervened since their 
creation, the inequalities on the surface of the 
earth would long ago have been worn down to 
a level. 

The axis of the earth would not experience 
any sensible change of position by the up- 
heaval of new mountains at different points 
on the earth's surface, as represented by 



42 GRAVITATION 

Newton, in his " Principia," Book I. Prop. 
66, for the reason that the inequalities would 
balance each other. New mountains cannot 
be uplifted without there being somewhere 
equivalent new depressions. Again, if by any- 
gradual denudation and overloading, the 
width of the Atlantic should be sensibly re- 
duced, land would be upheaved in the Pacific 
ocean. 

XXVII. 

Where Leveling Forces are Most Active. 

The leveling forces are not acting rapidly 
on the rocks that lie above the line of perpet- 
ual frost, as is evident from their jagged ap- 
pearance ; but a little below this line these 
forces are working with great energy, mani- 
festing their effects in the heaving of the 
surface, the result of alternate freezing and 
thawing, and in the action of glaciers and 
torrents. The more violent action of these 
forces sometimes culminates in the loosening 
of large quantities of material, the formation 
of overhanging cliffs, or the frightful move- 
ments of immense avalanches of earth and 
rock. As these masses of rock and earth find 
a lower level their weight is increased ; and 
as they are transported to a greater or less 



THE DETERMINING FORCE. 43 

distance, they, to a greater or less degree, de- 
range the geographical landmarks, by their 
effect in lightening or overloading. 



xxvin. 

Sustaining Strength of the Earth's Crust 
Levhted. 

Although the arched form of the crust 
gives it firmness and stability, its sustaining 
strength is limited, because the ability to re- 
sist a crushing force that exists in the foot of 
the arch and in the base of the vertical col- 
umn is limited. The solidity and sustaining 
strength of the crust are such, with its very 
slight elasticity, that it resists, for a while, 
this gradually leveling process, before fractur- 
ing and yielding to the forces that compel it 
to take a new position. This resistance causes 
the changes of level, and the transition in the 
density of the matter to be more or less par- 
oxysmal, rending the solid crust, producing 
shocks or earthquakes, by the fracture and 
concussion, at times forming new volcanoes, or 
reviving old ones. 



44 GRAVITATION 



XXIX. 

Causes Modifying Disturbance Kesulting 
from Fracture. 

The disturbance produced when the crust is 
fractured varies with the nature of the soil, 
the face of the country, and the height at 
which fractures occur. The motions imparted 
to the crust on the line at which faults are 
formed are very complicated and violent, as a 
portion of the crust on that line is being up- 
lifted, and a portion depressed. When the 
crust is fractured there is more or less of the 
lateral motion of opening and closing. These 
complicated motions and disturbances of the 
solid crust occasionally show their devastating 
power in frightful earthquakes and other sim- 
ilar catastrophes. When the egress from the 
vents is unobstructed, the disturbing effect of 
the concussion on the surrounding crust is 
somewhat lessened. Secondary causes are 
sometimes introduced, as when fluids pour 
into the fractures of the crust, and are quickly 
converted into steam and gases by the intense 
internal heat. 



THE DETERMINING FORCE. 45 

XXX. 

Conditions under which Earthquakes are 
Specially Liable to Occur. 

Earthquakes occur most frequently where 
the disturbing forces are the most intense, and 
act the most in unison, as when the earth is in 
that part of her orbit nearest the sun, and the 
moon is at her least distance from the earth ; 
or when the sun, moon, and planets are in the 
same line with the earth, and a high tide, in 
consequence, rests on the area about to be de- 
pressed, as was the case in the recent earth- 
quake in Charleston, S. C. ; or when there is 
a sudden decrease in the pressure of the at- 
mosphere on the continent, or on a portion of 
the continent and ocean. These conditions 
are greatly modified by the instability of the 
earth's axis ; a topic to be considered in a 
subsequent chapter. The fall of the mercury 
in the barometer one inch would indicate a 
diminution of atmospheric pressure equal to 
the removal of a little more than one foot of 
water. So far as this should be over the con- 
tinent, its full force would be felt in the change 
of surface pressure ; but if it were over the 
ocean, the remoter waters would tend to flow 
in, on account of the greater pressure to which 



46 GRAVITATION 

they would be subjected, and thus the weight 
would be kept nearly uniform on those por- 
tions that were being depressed. 

There are atmospheric tides also, corre- 
sponding with the tides of the ocean. When 
these tides are at their maximum at a given 
locality on the ocean, other circumstances 
being favorable, the ebb of the atmospheric 
tide causes the barometer to be at its minimum 
on the adjoining continent. 

As the sun passes the equator twice every 
year, and the spring tides are the highest 
when the sun is in that vicinity, earthquakes 
are frequent when the sun is near the equi- 
nox. 

As the land surface is more largely situ- 
ated in the northern hemisphere, and as this 
has the least amount of snow and ice resting 
upon it when the sun is at his greatest north- 
ern declination ; and as the disturbances have 
been accumulating during the year, and the 
vertex of the tidal wave tends to follow the 
sun's course in his journey to and fro across 
the equator, earthquakes are liable to occur 
when the sun approaches the northern summer 
solstice. 






THE DETERMINING FORCE. 47 

XXXI. 

Varying Distances, Centrifugal and Cen- 
tripetal Forces. 

Irrespective of the conditions which control 
the expansive force of heat, a permanent in- 
crease or decrease of gravitation would cause 
a corresponding increase or decrease in the 
density of matter. When the distance be- 
tween the sun and any of the planets is di- 
minished, the centripetal and centrifugal 
forces acting upon these planets are aug- 
mented. As these forces act upon matter in 
opposition to each other, their tendency is 
to increase or reduce the density of the bodies 
upon which they act, in the ratio of the in- 
crease or reduction of these forces. 

As a result of the great eccentricity of the 
orbits of comets, and the extreme tenuity of 
their substance, there is a sensible reduction 
in some of their disks, as they approach the 
sun ; another result may be that some of them 
by compression become self-luminous. As the 
distances between the sun, moon, and earth 
are continually changing ; and as the matter 
of the earth is alternately approaching, and 
receding from, the sun and moon, by the 
earth's motion on its axis and in its orbit, 



48 GRAVITATION 

the density of the earth is slightly affected by 
these varying influences. These disturbing 
forces cause sensible continuous motion of the 
melted matter in volcanic vents. 

XXXII. 

Volcanic Vents. 

As the artisan is not able to braze up the 
last aperture in the thin shell of a hollow me- 
tallic globe a few inches in diameter, on ac- 
count of the continually varying pressure 
on the inner and outer surfaces ; so nature 
fails to refrigerate the melted matter in vents, 
and thus close up the last apertures in the 
crust, on account of the constant movement 
of the molten matter in the vents, caused by 
the ever-varying pressure upon its inner and 
outer surfaces. For this reason we must ex- 
pect that volcanoes will continue. If the 
fluid nucleus could remain in a state of rest, 
the uniform pressure of the solid crust acting 
upon it would force it up through every vent 
and fissure, to a height nearly equal to that 
of the fluid surface before any refrigeration 
and contraction took place. This conclusion 
is confirmed by results that may be seen in 
many localities on the surface of the earth. 
Owing to the continual motion of the melted 



THE DETERMINING FORCE. 49 

matter, by inertia it may be carried still 
higher and form cones above the original 
level. As the melted nucleus conforms to the 
center of pressure, and the sea maintains a 
level to that center, the height to which the 
fluid would rise above the surface of the earth 
should be calculated from the level of the sea, 
volcanoes being more likely to overflow at the 
sea-level and less likely on the higher points 
where the crust is thicker. The crust varies 
in thickness, owing to the variation in density 
and force of gravity, and to the unequal sus- 
taining strength of the spherical form of the 
crust in different districts and at different ele- 
vations. These inequalities and changes in 
the density of matter, and the varying egress 
of the fluid through the vents, giving different 
degrees of momentum, cause the melted 
matter to overflow, or to stand in the vents 
at different heights as regards the level of the 
sea. 

As dissimilar inferior strata are being con- 
densed and made fluid, at different periods, 
resulting from the transposition of matter on 
the surface, there may be a like variation in 
the substances ejected from the same volcanoes, 
or fissures, at different times. While granite 
may be the principal ingredient of the fused 



50 GRAVITATION 

nucleus, the various kinds of trap rock may 
appear as the result of the fusion of different 
strata. 

XXXIII. 

The Earth's Crust Thin, and the Interior 
Hot. 

That the crust is relatively thin, and that the 
interior below this crust is in a fluid condition, 
is evident from the inability of such matter, 
at the depth of a few miles, to resist the pres- 
sure of the superincumbent mass. If we con- 
sider the steady increase in the intensity of 
the forces that tend to develop heat as we go 
from the surface toward the center, in con- 
nection with the increase in the conductivity 
of the strata in the same direction, we shall 
see that the interior must be intensely hot. 
Although heat tends to a uniform diffusion of 
itself through a horizontal stratum of uniform 
density, yet when the density of any portion 
of such a stratum becomes sufficiently reduced 
to admit of refrigeration, the power of con- 
duction is nearly obliterated, so that it might 
remain congealed for ages, if its thawing de- 
pended upon heat received by conduction. 
This conclusion is sustained by the existence 
of permanently frozen wells, and by similar 
phenomena in various localities. 



THE DETERMINING FORCE. 51 

XXXIV. 

Possible Transitions of Heat and Matter. 

To illustrate the transitions through which 
the heat and the matter of the earth may 
pass, suppose that we take fifty parts of some 
fusible metal, and subject forty-nine parts, 
more or less, in a crucible to an intense heat, 
until it is an intensely hot fluid mass. If we 
should then add the remainder, it also would 
become fluid. So if the earth's crust could 
be broken up and pushed into the melted 
mass, the heat contained in this nucleus would 
restore the earth to its original fluid condition. 
But in process of time, the changes which it 
has undergone would be repeated, the heat 
would return to its present limits, and the 
whole earth would assume its present condi- 
tion. To maintain that if the entire earth 
were thus melted, the heat could not return to 
its present limits, would be to maintain that 
what now is is impossible. If it were thus 
melted, the matter composing the crust would 
be expanded, the inequalities of the surface 
would be leveled, and the diameter of the 
sphere enlarged ; but the surface of the earth 
would not be greatly increased, as will be ap- 
parent when we have made due allowance for 



52 GRAVITATION 

the undulations and surface wrinkles of the 
present formations, for the crust originally 
congealed when the matter was thus ex- 
panded. 

XXXV. 

Heat and Gravity Correlative. 

In establishing the law of the conservation 
of gravity and heat, it becomes necessary to 
show that heat disappears from, or increases 
in, two bodies, as they approach, or recede 
from, each other, in the same ratio as the 
force of gravity affecting them increases or 
decreases. Gravitation is a force varying in- 
versely as the square of the distance, and when 
it is resisted heat becomes its equivalent. 
When two bodies are attracted toward each 
other, the equivalent of the force of gravity 
is found in their accelerated motion. When 
that motion is resisted by any force, matter is 
condensed, and heat, the equivalent of the 
condensing force, is made sensible. 

If we should remove a quantity of matter 
from any locality on the surface of the earth, 
a portion of the fluid nucleus underlying that 
locality would expand and heat proportionate 
to the force of compression removed would 
disappear. The solidity of the crust would 



THE DETERMINING FORCE. 53 

resist a transition under a particular locality, 
causing the expansion at the interior to ex- 
tend over a larger surface, but the melted 
nucleus would be diminished by the removal. 
If the matter thus removed were attached to 
a balloon, and carried to the upper regions of 
the atmosphere, the loss of heat in the portion 
of the fluid nucleus underlying the locality 
from which the matter had been removed 
would be the same, and heat would have van- 
ished from that locality and the elevated body 
would rest in an atmosphere less dense than 
that from which it had been taken. As the 
conductivity of a homogeneous stratum of 
uniform density favors the diffusion of a uni- 
form temperature in a horizontal direction, 
the temperature of the elevated mass would 
be reduced to that of the medium in which it 
rests, and the frosts of perpetual winter might 
abide upon it. But if the elevated mass had 
a rigid texture that would prevent its expan- 
sion in an equal ratio with the loss of gravity, 
then force, the equivalent of heat, would not 
vanish in the same ratio. This will be appar- 
ent if we imagine the mass to be carried up 
beyond the influence of the earth. In this 
case, while gravity has diminished as the square 
of the distance has increased, the stored heat 



54 GRAVITATION 

of the mass has not vanished in the same 
ratio, for the tendency to expand has been re- 
sisted. We see then that by elevating a body, 
and thereby causing gravity to decrease, we 
do not remove the force of cohesion. 

XXXVI. 

Relation of Gravity to Cohesion. 

As matter must have existed before gravity 
condensed and gave it form, the action of 
gravity must have been antecedent to that of 
cohesion. As the effects of gravity were felt 
before cohesion began to act, so gravity must 
cease to act before cohesion will give way. 
As cohesion originally fixed its firm grasp on 
the particles of solid matter as the result of 
refrigeration when the matter was subject to 
the condensing effect of gravity, heat must 
be restored to matter that it may expand after 
the condensing power of gravity shall have 
been removed. If to the body elevated be- 
yond the influence of gravity, we should re- 
store the heat that belonged to it before 
refrigeration, the body would be fused, cohe- 
sive force, the equivalent of heat, would van- 
ish, and, as a consequence, the body would 
undergo a corresponding expansion. The 



THE DETERMINING FORCE. 55 

more rare the same substance, the greater is 
its capacity for force, the equivalent of heat, 
per pound. 



XXXVII. 

Effect of the Removal of Gravity. 

As matter existed prior to its condensa- 
tion by gravity, it might continue to exist 
should gravitation be removed. Gravity has 
been constantly producing its effects on the 
earth since the creative act ; and, as we are 
led to believe by Holy Writ 1 that the force of 
gravitation has been suspended from a limited 
amount of matter, let us, for a moment, con- 
sider what the effect would be if all the matter 
composing the earth should be miraculously 
set free from the influence of gravitation. If 
it should be gradually set free, 2 the melted 
nucleus would expand, breaking the crust 
into fragments, and as these fragments would 
retain the greater density given them by pres- 
sure, they would sink, and as heat would 
tend toward the denser matter, they would 

1 Ex. xiv. 22 ; 2 Kings vi. 6 ; Matt. xiv. 26-29 ; and sim- 
ilar passages. 

2 If the release should be rapid, fragments of solid mat- 
ter corresponding to that of meteors might be hurled into 
surrounding space. 



56 GRAVITATION 

necessarily be melted. Under such condi- 
tions, the prophecy in regard to the final 
consummation of all things would be liter- 
ally fulfilled. The heat that withdrew from 
the crust, when under the condensing power 
of gravity, would be restored. The elements 
would "melt with fervent heat and be dis- 
solved," and the expansion would cause the 
earth to " pass away with a great noise." 
Gravity, cohesion, and heat would vanish, and 
matter would be greatly rarefied. While grav- 
itation has power to condense the rarest neb- 
ulous matter, and so produce heat, heat, in 
turn, has power to expand the same matter to 
its original nebulous condition, when released 
from the influence of gravitation. 

XXXVIII. 

Consequence of the Kestoration of Gravity. 

As we have not supposed any suspension of 
the translating forces, if after the wide separa- 
tion of the particles of matter composing the 
earth, resulting from their release from the 
influence of gravitation, they should again be 
brought under its original power, then nature, 
with her present laws, would restore the pres- 
ent density, figure, and physical condition of 



THE DETERMINING FORCE. §7 

the earth, but not, perhaps, its present geo- 
graphical features. Matter would be con- 
densed and a melted mass would be produced. 
That portion of matter forming the surface, 
being the least dense, would soonest lose some 
of its heat, would be refrigerated and form a 
crust. 

XXXIX. 

Peocess of Eefeigeration. 

As the ruins left by some great conflagra- 
tions retain their heat for months ; and as 
several years are often required to complete 
the refrigeration of matter a few feet in thick- 
ness that has been ejected from a volcano dur- 
ing a single eruption ; what ages must have 
elapsed during the refrigeration of the solid 
crust of the earth ; epochs during which the 
temperature was gradually decreasing on the 
surface. If the crust had not been disturbed, 
all portions would sustain force and retain 
heat proportionate to the density and conduct- 
ing power of the strata in which they were 
severally formed. As it is, all portions have 
retained heat proportionate to their primitive 
density and conductivity, but modified by the 
normal density and conductivity of the strata 
to which they have been transferred. Since 



58 GRAVITATION 

the interior is subject to an immense pressure, 
it must be intensely hot, and this the economy 
of nature demands, in order to maintain motion 
in the fluids, and vitalize all nature. On ac- 
count of the centralizing tendency of heat, if 
the nucleus were not intensely hot, the surface 
would be intensely cold. 



XL. 

Equalization of Temperature. 

The constant transposition of the fluids of 
the earth tends to the equalization of heat, as 
is shown by the direction and temperature of 
the prevailing currents. The currents in the 
atmosphere tend to equalize its temperature ; 
while its conductivity and capacity to sustain 
pressure increase with its density, thereby in- 
creasing the refrigerating forces. Hence, a 
dense atmosphere, on a clear evening, facil- 
itates the deposit of dew, or the production of 
frost. 

XLI. 

Direction and Form of Inequalities, How 
Determined. 

In consequence of the centrifugal force and 
the spheroidal figure of the earth, the ten- 



THE DETERMINING FORCE. 59 

dency originally must have been to form the 
inequalities on the earth's surface nearly par- 
allel with the equator. But the unequal tem- 
perature, and the equalizing tendencies of the 
air and the water on different portions of the 
earth, cause a constant transference of the 
fluids between the poles and the equator, 
maintaining a constant series of currents at 
right angles to the equator, and by means of 
them wearing away the intervening barriers, 
giving outline and form to the continents, and 
tending to determine the direction of moun- 
tain chains. 

XLn. 

Ocean Currents Modified by Earth's 
Motion. 

Every thing in the universe is in motion, 
and all matter moves in curves. The equa- 
torial waters are being carried forward, by the 
rotation of the earth on its axis, about 1,040 
miles per hour, while the polar waters are 
nearly destitute of a progressive motion. It 
is, therefore, evident that the equatorial cur- 
rents flowing north or south would tend to 
the eastward of a meridian line, and that the 
polar waters flowing toward the equator would 
tend toward the westward of such a line. By 



60 GRAVITATION 

a composition of forces, the currents in seas 
and oceans are made to move more or less in 
curves as is represented in Fig. 2. Let Q R 
represent the plane of the equator, P the north 
pole, and P A the polar current flowing south 
to A, and W N the equatorial current flowing 
north. If we could now introduce a central 
gravitating force by drawing the water off 
through an opening at C, the water would 
have a spiral motion 
as represented by N 
and A B. The ten- 
dency to a rotary mo- 
tion as the resultant of 
unequal translating ve- 
locities, when taken in 
Fig. 2. \ .,, 

connection with a cen- 
tral motion, may be seen when quiescent water 
is drawn off from a bathing tub. Observation 
will show that, in the northern hemisphere, 
there is a tendency to a left hand rotary 
movement, and in the southern, to a reverse 
movement. Hence, by so simple a phenome- 
non as the behavior of running water in our 
houses, we can discover evidence of the earth's 
rotation on its axis, and also whether the lo- 
cality of observation is north or south of the 
equator. Currents in the ocean become very 




THE DETERMINING FORCE. 61 

complicated in consequence of a diversity of 
causes of which we may name the following : 
1st, Variations of temperature due to difference 
in locality, depth of water, and nearness to the 
coast line ; 2d, The friction and momentum of 
opposing currents, as when the Gulf Stream 
encounters the waters flowing out from Davis 
Straits ; 3d, The changing currents of wind ; 
4th, The tendency of gravitation to maintain 
a perfect sphere while the centrifugal force 
and the instability of the earth's axis are tend- 
ing to pile up the water over the equator to 
the height of about thirteen miles. 

XLIIL 

Inequality of Temperature a Cause of 
Springs. 

The unequal temperature and density of 
water in the earth causes springs. If we 
apply heat to the lower stratum of a column 
of water, the equalizing tendency is made vis- 
ible by two currents, — the warm current 
ascending, and the cold current descending. 
Thus we see how the internal heat produces 
motion, and causes springs. We may also 
infer that artesian wells would overflow at, or 
above, the surface of the earth, if it were a 



62 GRAVITATION 

perfect sphere, since it would stand higher in 
the ascending column. The variation in the 
height of two columns of water that balance 
each other depends upon their length, and on 
the inequality of their temperature, since this 
determines their relative specific gravities. 
A variation in temperature may occasion a 
variation in height to the extent of one foot 
in twenty-three, or over four feet in one hun- 
dred. 






THE DETERMINING FORCE. 63 



CHAPTER II. 

THE THEORY OF THE TIDES. 
XLIV. 

Influence of Sun and Moon upon the Tides, 
as Presented by Different Writers. 

The cause of tides has long been a contro- 
verted subject. The ancients very naturally 
attributed the causative agency to the moon, 
since the position and altitude of the tides 
maintain nearly a constant relation to that 
satellite. After the law of gravitation was 
finally established by Sir Isaac Newton, he 
sought to prove in the " Principia," Book III. 
Props. 36 and 37, that the gravitating influ- 
ence of the sun and moon on the waters of 
the ocean would elongate the fluid belt that 
encircles the earth sufficiently to produce the 
ebb and flow of the tides ; but he calculates 
the density of the moon to be more than 
double its true density. Mathematicians of 
later date have decided that the "lifting 
power of the moon would not raise the water, 
or produce a tide of more than .07 of an 



64 GRAVITATION 

inch, were the ocean 10,000 fathoms deep ; 
and that the disturbing energy of the tan- 
gential force, at its maximum, is only three 
fourths of the maximum lifting force." 

In their explanations of the tides, the writ- 
ers of our text-books on Physical Geography 
and Astronomy present diagrams and make 
statements to show that there would be a 
high tide formed under the disturbing body, 
even if the earth did not rotate on its axis. 
Sir John F. W. Herschel says, " were the 
earth indeed absolutely fixed, held in its place 
by an external force, and the water left free 
to move, no doubt the effect of the disturbing 
power would be to produce a single accumula- 
tion, vertically under the disturbing body." 

XLV. 

Causes Assigned Inadequate to Produce the 
Effect. 

The tangential and lifting force of the 
moon is so inadequate to produce the tidal 
wave that it would not have been noticed if 
there had been no rotation of the earth upon 
its axis. If we explain the tides in accordance 
with the hypotheses advanced in our text- 
books, we do not find that relation of cause 



THE DETERMINING FORCE. 65 

and effect that should exist when we compare 
the effect produced by the moon with the 
corresponding effects produced by other 
forces of nature. 

The variation of an inch in the mercurial 
column of the barometer is equal to the vari- 
ation of 13 1 inches in a similar column of 
water. As the range of variation in the 
height of the mercurial column is between 
two and three inches, and this variation is due 
to changes in the density of the atmosphere, 
these changes should raise a tide in particular 
localities about forty times as high as the 
direct lifting force of the moon coidd do. If 
the comparatively feeble tangential force of 
the moon has any sensible effect in piling up 
the waters of the ocean, what vastly greater 
effects should we expect from the wind when 
it sweeps over the surface of the ocean 
toward the coast, at the rate of one hundred 
miles an hour, with sufficient force to prostrate 
the sturdy oak, and lay low extensive forests. 
The action of the wind, it is true, is confined 
more particularly to the surface, but the 
rapidity with which it forms and reverses the 
currents of the ocean indicates that it would 
drive in the waters of the ocean much faster 
than they could possibly return by an under- 



66 GRAVITATION 

current, on account of the large amount of 
friction the returning inferior current must 
encounter on its entire surface. The lateral 
force of the wind should overcome the resist- 
ance as effectually as the gravitating influence 
of the moon does. 



XLVI. 

Eelative Force of Different Elements. 

The variation in the pressure of the atmo- 
sphere over a specified locality should cause, 
at times, an elevation or depression in the 
waters of the ocean of nearly three feet. The 
disturbing effect of these elements should, 
therefore, if the adopted theories were correct, 
not only have their accredited effect on the 
oscillations of the ocean, but when they act 
in unison in favorable localities, they should 
exceed the effects of the sun and moon in 
causing the ebb and flow of the waters, and 
their results should be as much more marked 
as their measurable forces are more potent 
than are those of the sun and moon. That 
the causes of the tides are not satisfactorily 
explained, at least to some minds, is frankly 
admitted by many who adopt the present 
popular explanations. 



THE DETERMINING FORCE. 67 

Herschel says, " Many persons find a 
strange difficulty in conceiving the manner in 
which they are produced. That the sun or 
moon should by its attraction heap up the 
waters of the ocean under it, seems to them 
very natural. That it should, at the same 
time, heap them up on the opposite side 
seems, on the contrary, palpably absurd." 

It is said that the tides are principally 
caused by the unequal attraction of the moon 
on the earth, and on the waters on its oppo- 
site sides. But the moon is only about one 
eightieth the mass of the earth, and attracts 
the waters on the earth nearly 3,600 times 
less powerfully than the same amount of 
matter in the earth attracts it, since it is 
nearly 240,000 miles distant. The moon, 
then, with its comparatively feeble force of 
gravitation is said to draw up the waters of 
the ocean nearly under it, ten feet more or 
less in height, while it draws the whole mass 
of the earth away from the water on the op- 
posite side five feet, causing a tidal wave of 
equal height with the other by the lagging 
of the water. Yet the moon attracts the 
water on the side of the earth remote from 
itself with nearly as much force as it does 
that on the nearer side, since only a small 



68 GRAVITATION 

fraction of its attractive force is lost by pass- 
ing through the earth. According to this 
hypothesis, the attraction of the moon, acting 
in unison with terrestrial gravitation, is not 
powerful enough to hold the water down to 
its normal level on the remoter side, while, 
acting in opposition to terrestrial gravitation, 
the moon raises a tidal wave five feet high on 
the nearer side of the earth. At a point on 
the side of the earth remote from the moon, 
where a high tide culminates, the water of 
the ocean is drawn by terrestrial gravitation 
toward the center of the earth, with a ve- 
locity sixty times as great as that with which 
the moon is drawn toward the earth ; and 
this latter velocity is about eighty times that 
with which the earth is drawn toward the 
moon. What, then, is to prevent the water 
on the remote side of the earth from being 
attracted toward the earth's center by gravi- 
tation as fast as the earth is falling toward 
the moon ? In the theory of the tides 
adopted by Herschel and others, in accounting 
for the high tide on the remoter side of the 
earth, it would seem that the force of terres- 
trial gravitation is ignored, while according 
to Newton, " Principia," p. 452, " the moon's 
force to move the sea is to the force of 



THE DETERMINING FORCE. 69 

gravity as 1 to 2,871,400. It is evident that 
this force is far less than appears sensibly 
in statical or hyclrostatical experiments, or 
even in those of pendulums. It is in tides 
only that this force shows itself by any sen- 
sible effect." We must take into account the 
fact that Newton considered the density of 
the moon compared with the density of the 
earth as 11 to 9, while the later tables give 
the density of the moon 0.565 7, that of the 
earth being 1. 

XL VII. 

Influence of the Earth's Rotation. 

In proof that " the waters are raised by the 
difference of the moon's attraction on the 
superficial waters on both sides, and on the 
central mass," Herschel says : " In the theory 
of the moon, the difference of the sun's attrac- 
tion on the moon, and on the earth, gives rise 
to a relative tendency in the moon to recede 
from the earth, in conjunction and in oppo- 
sition, and to approach it in quadratures." 
The planets are poised between the centrip- 
etal and contrifugal forces, and any slight 
disturbing force enters into composition with 
them, and soon causes a sensible perturbation. 
But the water on the opposite sides of the 



70 GRAVITATION 

earth's surface is subject to conditions quite 
different from those that determine the mu- 
tual relations of two independent bodies in 
space. In the former case their behavior is 
really determined by the overwhelmingly pre- 
dominant force of terrestrial gravitation draw- 
ing them to a common center. 

The unequal attraction of the sun and 
moon on the opposite sides of the earth may 
tend to elongate the 
belt of water encircling 
it ; but this unequal 
attraction is so slight 
a disturbing influence, 
when compared with 
other disturbing forces 
introduced by the ro- 
tation of the earth on 
its axis, that acting: 




Fig. 3. 



alone it might never have been perceptible in 
the oscillations of the ocean. This is the 
more apparent, when we consider that the 
points at which the tides culminate are chang- 
ing their positions on the equator nearly 1,040 
miles per hour, and that a force vastly greater 
than that assigned is necessary to cause the 
ebb and flow of the tides. But if the laws 
of dynamics are duly considered, in conuec- 



THE DETERMINING FORCE. 71 

tion with the influence of the sun and moon, 
I believe that the phenomena of the tides will 
be more correctly explained. 



XLVin. 

Eesultant of the Seyekal Elements. 

If we place a particle of matter at P, Fig. 
3, and give it an impetus toward G, its path 
will be rectilineal, if there is no disturbing in- 
fluence to cause deviation. Let M represent 
the moon, and place the particle again at P ; 
now give it an impetus that would carry it in 
a right line to B. Suppose that while this 
impetus was carrying it over the distance 
PB, the attraction of the moon would draw 
it up a distance equal to PG ; then, by the 
composition of these forces acting together, 
the particle would be carried over the diag- 
onal PP 1 of the parallelogram PGFB. Now 
let us suppose the influence of the moon to be 
suspended; let ZON represent the earth with 
the pole projected toward the observer; let 
the particle be placed again at P, and while 
it is subject to the continuous attraction of 
the earth, give it an impulse, as before, that 
would be sufficient to carry it over the line 
PB ; it will be deflected to the earth at some 



72 GRAVITATION 

point, as P 2 . Now place the particle again at 
P, and while it is under the attraction of both 
the earth and moon, give it a like impulse as 
before ; it would now be deflected into a 
different path as PP 3 . The particle P may 
represent water at the equator of the earth 
at P 4 , with a velocity of nearly 1,040 miles 
per hour, and moving for twelve hours be- 
tween the earth and moon, till it is brought 
by the rotation of the earth on its axis to the 
position P 5 . As from P 4 to Z the water is 
failing toward the moon, it is gaining a mo- 
mentum that would be more or less tangen- 
tial after it passed the point Z, and would 
produce its maximum effect at some point, as 
P 3 , as from P 3 to it would be retarded by 
the action of the moon. The uplifting forces, 
therefore, combine to form a high tide at P 3 
nearly 45° from a direct line joining the cen- 
ters of the revolving and disturbing bodies. 

XLIX. 
Reciprocal Motions of Earth and Moon. 

As the quantity of matter in the earth is 
about eighty times as great as that in the 
moon, their common center of gravity is about 
eighty times nearer the former than the latter, 



THE DETERMINING FORCE. 73 

and is therefore situated about 3,000 miles 
from the center of the earth, and is repre- 
sented at E, Fig. 3. The earth completes a 
revolution around the moon on the point E in 
the same time that is required by the moon to 
complete a revolution around the earth. The 
mean distance between the moon and the 
point E is invariable, and the motion of the 
earth around the moon may be said to be 
hinged on that point. Let the plane of the 
line LN divide the earth into two equal sec- 
tions. In the revolution of the earth on its 
axis, the section P 2 P°0 has a motion from the 
moon, while the opposite section QP 4 1 has a 
motion toward it. 

The mean distances between the moon and 
the points Z and N are not affected by the 
motion of the earth around the moon, since 
Z, N, and E are on the same line ; and the 
points Z and N have no motion either to or 
from the moon. The axis of rotation is then 
equidistant between Z and N, but as the 
earth is falling around the moon on the point 
E, the center of the earth, C, and the point R 
are moving respectively in the orbits CO 1 and 
RT. Hence R has a greater velocity toward 
P 4 than P 3 has toward P 5 . 



74 GRAVITATION 



L. 

Instability of the Earth's Axis, and its 
Effect. 

The line in the earth that has the least mo- 
tion, I shall designate as the axis of rotation. 
That line does not pass through the true 
center of the earth, but at a little remove 
from it as is represented at A, Fig. 3. As its 
angular position from a line joining the moon 
and the center of the earth remains invariable, 
the retrograde motion of the moon, when 
compared with the rotation of the earth on its 
axis, causes an instability of the earth's axis 
and gives an eccentric motion to the earth. 
The longer portion is in the direction P 4 , the 
shorter towards P 5 , and the greater centrif- 
ugal force engendered on the longer portion 
tends to form a high tide at R. The accumu- 
lation of the waters at P 3 and their retarda- 
tion from this point to causes an ebb tide 
at the latter point ; and the increased centrif- 
ugal force on the longer portion of the eccen- 
tric, tending to raise the waters at R, has a 
tendency to cause an ebb tide at O 1 . The 
tendency of the water to flow on from P 3 by 
inertia, and form a high tide on the shorter 



THE DETERMINING FORCE. 75 

portion of the eccentric at P 5 , is counterbal- 
anced by the decrease in the centrifugal force, 
which allows an equal flow in a transverse 
direction toward the poles. 



LI. 

Result weee the Position of the Earth's 
Axis Invariable. 

If the center of the earth, C, had as rapid a 
motion of translation in its orbit, CO 1 , around 
the moon, as R, Fig. 3, has in its orbit, RT, the 
rotating velocity of R toward P 4 would be 
no greater than that of P 3 toward P 5 . The 
diameter P 4 P 5 would then rotate on a true 
and fixed center, C, and in this condition, as 
Herschel says, " the rotation must be per- 
formed round an axis or diameter of the 
sphere, whose poles or extremities, where it 
meets the surface, correspond always to the 
same points on the sphere." But this re- 
quires that the axis of a revolving body have 
a fixed position in space, or that every por- 
tion have an equal motion of translation, 
which does not admit of an orbital motion, 
but requires that the revolving body move in 
a rectilineal path. The curvilinear path of 
the moon, with its balanced condition, causes 



76 GRAVITATION 

the moon to have an axial rotation, giving al- 
ternate clay and night to the inhabitants of 
the moon, if such there are. 



LIL 
Cause of Axial Rotation. 

When all portions of a body moving con- 
tinually in a given direction have not equal 
velocities of translation, the resultant is a 
motion of rotation on an axis, as well as in an 
orbit, as is evident in the case of the moon. 
In Fig. 3, let I represent the inferior point of 
the moon, and I 1 the orbit in which it moves 
when passing around the earth ; let S repre- 
sent the superior point and SS 1 its orbit. It 
is evident that the point S passes around the 
point I during each revolution of the moon 
in its orbit, and that the excess of the trans- 
lating velocity of the point S over that of the 
point I must be such as to allow S to gain 
over I a distance equal to the circumference 
described about I as a center, with a radius 
equal to the line SI. 

Again, the axis of rotation in a revolving 
body is located in the line of the least centrif- 
ugal force; its position in the moon is indi- 
cated at I, in the earth, at A. It is well 



THE DETERMINING FORCE. 77 

known that solar and sidereal time coincide 
only at certain intervals ; the variation in one 
year is due to one revolution of the earth on 
its axis. 

As the rotating velocity of S is greater 
than that of I, the centrifugal force developed 
in the superior or longer limb of the eccentric 
must exceed that developed in the inferior or 
shorter, for this force increases with the ro- 
tating velocity when the periodic times are 
equal. As a portion of the earth is falling to- 
ward the moon while the moon is falling to- 
ward the earth, the unequal centrifugal force, 
which is proven to exist on opposite limbs of 
the moon, determines the fact of the existence 
of unequal centrifugal force on the opposite 
limbs of the earth. 

LIII. 

Projectile from a Bifled Gun. 

A condition may be conceived, when a 
deviation from a rectilineal path will not dis- 
turb the axis of rotation, as when a projectile 
is hurled from a rifled gun ; or if by chance a 
planet should move pole foremost in its orbit, 
and if the centrifugal force developed by its 
axial rotation should be sufficient to hold its 
equator invariably in the same plane. This 
may be illustrated by Fig. 4. 




78 GRAVITATION 

Let B represent a projectile as having 
moved through an arc of 90° to B 1 . The 
sides of the ball, BC and B 1 ^, in going from 
B to B 1 , will have passed through equal 
spaces in equal times, as is 
represented by the dark and 
the dotted line, as these lines 
are of equal length and 
come in contact with the 
ball at corresponding points. 
Fl g- 4 - Or, in the same Fig., A may 

represent a planet whose orbit is ABB ! D. 
Let NS represent the axis of rotation, N the 
north and S the south pole ; now suppose that 
as it advances in its orbit from A to B 1 the 
north pole is foremost, and that from B 1 to 
A the south pole. In this case the axis of 
rotation will not become unstable through the 
influence of any disturbing force or because 
of any deviation from a rectilineal path, as 
all portions of the moving mass have equal 
velocities of translation, and that all rotating 
velocities exactly balance each other. In this 
example the surface of the rotating body is 
supposed to be uniform, and the density of 
opposite parts equal. 



THE DETERMINING FORCE. 79 

LIV. 

Exceptions to Hekschel's View. 

When Sir John F. W. Herschel, in his 
work on astronomy, was presenting the sub- 
ject of the precession of the equinoxes, he 
seemed to fear that his representation of the 
motion of the earth might lead some of his 
readers to believe that the axis of the earth is 
unstable, — a belief that would have been in 
accord with facts. He says : " The reader 
will take care not to confound the variation 
of the position of the earth's axis in space, 
with a mere shifting of the imaginary line 
about which it revolves in its interior. The 
whole earth participates in the motion and 
goes along with the axis, as if it were really 
a bar of iron driven through it. That such is 
the case will be proved by two great facts. 
First : That the latitudes of places on the 
earth, or their geographical situation with re- 
spect to the poles, have undergone no percep- 
tible change from the earliest ages. Second : 
That the sea maintains its level, which could 
not be the case if the motion of the axis were 
not accompanied with a motion of the whole 
mass of the earth." The consideration of 



80 GRAVITATION 

the first of the above mentioned facts will be 
deferred to a subsequent chapter. But the 
ebb and flow of the tides demonstrates the 
fact that the sea does not maintain its level ; 
and this result is partly due to the fact that 
the movement of the axis in space is not ac- 
companied by a like movement of the whole 
mass of the earth. We have shown in sec- 
tion XLVIII. how this variation operates to 
produce the tides. 

LV. 

A Complex Problem. 

When we compare the centrifugal force 
which should be apparent on the longer por- 
tion of the eccentric, with that which perpet- 
ually uplifts and sustains the water over the 
equator nearly thirteen miles in height, the 
tidal wave may seem much less than what we 
ought to expect. On the other hand, the 
fact is, that although the unequal attraction 
of the sun and moon may uplift a tidal wave 
to the height of a fractional part of an inch, 
it is entirely inadequate to sustain the burden 
laid upon it by the popular hypothesis, of 
accounting for the daily observed results. 
Again, in forming an estimate of the results 
that would be produced by the action of a 



THE DETERMINING FORCE. 81 

given force, it becomes necessary to take into 
account the obstacles with which that force 
must contend. This will at once make it ap- 
parent that a force vastly superior to that as- 
signed will be required to raise a tidal wave 
in the ocean a few feet in height, as the point 
at which the tide culminates changes its place 
in longitude on the equator at the rate of 
nearly 1,040 miles per hour. As we proceed in 
the investigation, the great difficulty of reach- 
ing definite conclusions as to the height of the 
tidal wave that should result in any particular 
locality, from the action of any assigned force, 
becomes very evident. Many mathematicians 
and practical engineers have bestowed great 
care and much patient labor on the problem 
of the flow of water in channels with a given 
depth, width, and head. But suppose that 
they were to solve independently the problem, 
How long a time would be required for the 
accumulated waters over the equatorial regions 
to flow back toward the poles, and leave the 
earth a perfect sphere, if we suppose the rota- 
tion of the earth on its axis to be suspended 
without any immediate disturbance of the 
waters from such suspension ? 

When we consider the inconstant factors 
involved, such as the infinite variations in the 



82 GRA VITA TION 

depth of the ocean, variations that cannot be 
reduced to law ; the ever-shifting direction and 
magnitude of ocean currents ; the equally di- 
verse and uncertain elements of resistance re- 
sulting from the changing outline of the 
coast ; and many other similar conditions, — 
should we not have reason to expect consider- 
able diversity in the conclusions which they 
would reach ? 

The great complexity of the actual problem 
of accounting for the phenomena of the tides, 
as they now exist, becomes apparent, when we 
consider the transverse positions of conti- 
nents; the ever-varying distances between 
sun, moon,^ and earth ; the frequent changes 
in the direction of ocean currents and in the 
pressure of the atmosphere. 

Again, the velocity of the water and its 
power to resist the disturbing forces conse- . 
quent on axial rotation varies with the lati- 
tude. Then, too, currents moving in north- 
erly and southerly directions, and tending to 
the formation or dispersion of a tidal wave, 
move more or less in curves, owing to the ro- 
tation of the earth on its axis. 



THE DETERMINING FORCE. 83 



LVI. 

Forces Considered, Adequate to Produce 
the Tides. 

Having thus noticed a few of the compo- 
nent forces which are evidently concerned in 
in the formation of a tidal wave, the manifest 
intricacy of the problem demonstrates the ne- 
cessity of establishing the tables of the tides 
in different localities by patient and persistent 
observation. Without further remarks, I 
shall assert that the forces which have been 
assigned in the preceding discussion, to ac- 
count for the ebb and flow of the tides, are 
quite adequate to produce the observed re- 
sults. 

The effect of the axial rotation of the earth, 
together with the influence of the moon, is 
piling up the waters of the ocean, forming 
a high tide nearly 45° back of the line joining 
the centers of the earth and moon, while the 
increased centrifugal force engendered on the 
longer portion of the eccentric, caused by the 
shifting of the earth's axis, is forming a high 
tide on the opposite side. 

The sun and planets also have an influence. 
The effect of the sun's attraction upon the 



84 GRAVITATION 

earth's axis will be noticed more fully in an- 
other chapter. 

LVII. 
Location of High Tides. 
As the earth has a motion of translation 
around the moon, on their common centre of 
gravity, represented at E in Fig. 3, some phil- 
osophers have attempted to account for a high 
tide near the nadir, by the increased centrifu- 
gal force occasioned by this motion. Accord- 
ing to this hypothesis, N must be situated on 
the longer portion of the eccentric, — which is 
not the case, — and centrifugal force, being a 
secondary one, cannot be producing its effects 
ahead of the longer limb, but they must be 
back of it, as is seen in the formation of a 
high tide at R, nearly 45° back from the 
longer part of the eccentric. Therefore, if 
this motion should cause a high tide at the 
nadir, it would culminate at 0, nearly 45° 
back of what would in that case be the 
longer part of the eccentric, and where the 
most rapid motion would be, instead of at 
R, nearly 45° in advance of the force which 
would by this hypothesis be producing it. 
As the mean distances between the moon and 
the points Z C and N are invariable, the earth 



THE DETERMINING FORCE. 85 

lias no motion toward the moon in that di- 
rection, and the unequal attraction of the 
moon on the earth could not produce the 
tides at the nadir. 



86 GRAVITATION 



CHAPTER III. 

PRECESSION, NUTATION, AND OBLIQUITY OF 
THE ECLIPTIC. 

LVIII. 
Precession. — Newton's Theoey. 

The motion of precession was known to the 
ancients, and modern works upon astronomy 
have made the subject familiar to the general 
reader. Sir Isaac Newton early encountered 
strong opponents to his then novel theory of 
gravitation. To silence them, and establish 
his theory beyond a reasonable doubt, he 
must have felt the necessity of accounting 
for all the observed motions of the heavenly 
bodies. The motion of precession, therefore, 
made imperative demands upon him for an 
explanation in harmony with his new theory. 

Newton, therefore, assigned, as the cause 
of precession, the effect of the attraction of 
the sun and moon upon the excess of matter 
in the region of the equator of the earth. 
This solution, which has been adopted by 
modern astronomers, can be presented so as to 



THE DETERMINING FORCE. 87 

make it appear very plausible. When the sun 
and moon are away from the equinoxes, their 
angular position to the redundant matter in 
the region of the equator is such that they 
may seem to attract it with greater force than 
they do the matter in the region of the poles. 
It should be noted here that the greater 
density of matter at the poles in a very small 
measure counteracts the effect of any excess 
of matter at the equator, and would, in the 
same degree, lessen the tendency of the un- 
equal attraction, whatever there might be, on 
the equatorial and polar regions to produce 
the observed motion of the poles. 



LIX. 

Influence of Redundant Matter at the 
Earth's Equator. 

If the redundant matter at the equator 
tends to follow the sun and moon because of 
any superior gravitating force inherent in it, 
over that of the matter at the poles, the re- 
sult must be a perpetual tendency to lessen 
the angle of inclination between the equator 
and the ecliptic, until they should be brought 
to perfect coincidence. For when the sun and 
moon are north of the equator, their action on 



88 GRAVITATION 

the excess of matter at the equator would 
tend to draw the ring of redundant matter 
into the plane of the ecliptic, depressing the 
north pole and elevating the south ; and when 
they are south of the equator, their action 
upon the excess of matter at the equator would 
tend to draw the ring of redundant matter 
into the plane of the ecliptic, and, as before, to 
depress the north pole and elevate the south. 
When the sun and moon are together at 
either equinox, or are both acting in the line 
of the equinoxes, their action could have no 
tendency to change the position of the plane 
of the equator. 

But that the poles of the earth do not have 
a motion tending to diminish the obliquity of 
the ecliptic was fully proved by Bradley ten 
years after Newton's death. He found that 
stars situated near the solstitial colure, that 
were nearly opposite in right ascension, ap- 
peared, at times, to undergo equal and oppo- 
site changes in declination, proving a nutation 
of the earth's axis, as if, applying Newton's 
theory, the moon, in certain parts of its orbit, 
repulsed, rather than attracted, the redundant 
matter at the equator. 



THE DETERMINING FORCE. 89 



LX. 

Fallacy of the Newtonian Hypothesis. 

In continuing the investigation respecting 
the Precession of the Equinoxes, the fallacy of 
the hypothesis under consideration becomes 
still more apparent. It is said that the action 
of the moon on the accumulated matter at the 
equator causes the poles of the earth to be 
" describing a circle or ellipse in the heavens 
around the pole of the ecliptic as a center/' 
causing what is known as the Precession of 
the Equinoxes. According to this hypothesis, 
when the j3ole in its circuit arrives at one ex- 
tremity of the ellipse the equator must be 
tipped in one direction, it would seem to 
follow that when the pole should arrive at the 
other extremity of the ellipse, the plane of 
the equator would tip in the opposite direc- 
tion. 

In this case, the motion of precession must 
be reversed during the circuit of the pole 
through a portion of its elliptical orbit. But 
observation shows a perpetual retrogression, 
of 50i" of a degree, more or less, per annum. 
The true cause of the retrogression of the 
equinoctial points from year to year, with the 



90 



GRAVITATION 



variation of the obliquity of the ecliptic, and 
the nutation of the earth's axis, will form the 
subjects of inquiry in the following chapter. 

LXI. 

Eeal Causes of Precession. 

In explaining the tides, it was shown in 
Fig. 3 that the part of the earth toward P 4 
had a motion toward the moon, and that P 5 
had a motion in an opposite direction, P 4 be- 
ing in the longer limb of the eccentric, and 
P 5 in the shorter limb ; and that the axis of 
the earth was in the position represented at 
A, on a line at right angles with the line L, 
which joins the center of the earth and the 
center of the moon. 




Fig. o. 



THE DETERMINING FORCE. 91 



LXH. 

Causes or Precession Illustrated. 

Let us take a northern position in the heav- 
ens on a line with the center of the earth, C, 
as represented in Fig. 5, the moon, M, being 
in conjunction with the sun, S, the sun being 
at the vernal equinox. Let the line L be 
drawn, joining the centers of the sun, moon, 
and earth. 

In this Fig. the axis of the earth's rotation 
is represented at A, and holds the same an- 
gular position to the center of the earth, C, 
and the line L as in Fig. 3. If we note the 
motion of the earth and moon as they move 
on in their yearly course, we shall find that 
when the earth has completed one revolution 
in its orbit, the moon has nearly completed 
the thirteenth revolution in its orbit, but has 
fallen a little back from the line L, and is at 
a position that may be represented by M 1 . 
Now let L 1 be drawn, joining the centers of 
the earth and moon at M 1 . The axis of the 
earth's rotation will have fallen back to the 
position A 1 , maintaining the same angular 
position to the center of the earth and the line 
L 1 that it had to the center and the line L. 



92 GRAVITATION 

The influence of the moon on the earth, as 
has been shown, causes the axis of rotation to 
be removed from the geometrical center of the 
earth, giving the latter an eccentric motion. 
The retrograde motion of the moon, when 
taken in connection with the diurnal rotation 
of the earth, causes the earth's axis to be un- 
stable, as it is continually dropping back to 
meet the moon. "While the earth's center 
comes up, at the end of the yearly revolution, 
to the line from which it started, the surface 
lags behind, in consequence of the eccentric 
motion caused by the instability of the earth's 
axis. 

LXIII. 

Amount of Annual Precession Variable. 

Astronomers have asserted that the amount 
of the annual precession of the equinoxes is 
not a constant quantity. In this they are 
doubtless correct, since it would be a neces- 
sary consequence of the fact that unequal 
portions of an eccentric must pass a given 
point in equal times. Astronomers have also 
asserted that the obliquity of the ecliptic is 
diminishing, but have failed to clearly define 
the cause, and to fix the limits of these varia- 
tions. 



THE DETERMINING FORCE. 93 

I will attempt to point out the positions of 
the heavenly bodies in which the variations 
are the greatest, and those in which they are 
the least, but a complete verification would 
require patient observation extended through 
a long period of time. 

Referring to Fig. 5, when the influence 
of the moon reaches the center of the earth 
from the position M 2 , the axis of the earth is 
at A 2 . The shorter limb of the eccentric is 
now passing under the sun, and when the in- 
fluence of the moon reaches the earth from the 
position M 3 , the axis is at A 3 , and the longer 
limb of the eccentric is then passing under the 
sun. When the shorter limb is approaching 
the sun, the falling back of the surface is de- 
creasing, and when the longer limb is coming 
up to the sun there is an opposite result. 1 

If the moon, represented at M 1 , should, at 
the end of the year, come up to the position, 
M, from which it started at the commence- 
ment of the year, the axis A 1 would come up 
to the position, A, from which it started : in 
that case there would be no annual precession. 
In other words, if the moon made any number 

1 Since the issue of the former edition of this treatise 
Professor Xe^vconib and others have reached the conclusion 
that the time of the earth's axial rotation is not exactly con- 
stant. Professor Newcomb in Siffiman's Journal, September, 
1874. 



94 GRAVITATION 

of complete revolutions in its orbit, while the 
earth is making one revolution in its orbit, the 
point 2 on the surface of the earth would 
have returned to 1, the point of starting, and 
all portions of the earth would have had equal 
motions of translation, and even rotation. 
But as the moon fails to come up at the end 
of the year to its starting-point, the axis rep- 
resented at A does not come up to the posi- 
tion A, and the dotted line 2 fails to come to 
the dotted line 1. The distance between 
these two lines, where they intersect the sur- 
face of the earth, represents the amount of 
the annual precession. This distance varies 
more or less from year to year. 

LXIV. 

Maximum and Minimum Eccentricity. 

When the sun and planets act in conjunc- 
tion with the moon, or when the distances 
between them and the earth are diminished, 
the axis of the earth deviates more from the 
true center, and the eccentricity is increased • 
so, also, when the sun and planets act in oppo- 
sition to the moon, or the distances between 
them and the earth are increased, the displace- 
ment of the axis of rotation and the conse- 
quent eccentricity are proportionately lessened. 



THE DETERMINING FORCE. 95 

The annual retrogression of the equinoctial 
points is at the maximum, when the influence 
of the sun, moon, and planets have their least 
distance, and reaches the earth from the posi- 
tion M 3 , as the longer limb of the eccentric is 
then passing under the sun. It is at the min- 
imum, when the sun, moon, and the planets 
are at their greatest distance from the earth, 
and their influence reaches the earth in the 
direction M 2 , as then the shorter limb of the 
eccentric would be passing under the sun. 
The instability of the earth's axis, however, 
depends mainly upon the disturbing influence 
of the sun and moon, since the independent 
influence of the planets must be very slight. 



LXV. 

Heeschel on the Stability of the Earth's 
Axis. 

In advancing the theory of the stability of 
the earth's axis, Herschel says : " The whole 
earth participates in the motion, and goes 
along with the axis as if it were really a bar 
of iron driven through it." " That such is 
the case," he says, " is proved by two great 
foots: 1st, that the latitude of places on the 
earth, or their geographical situations with 



96 GRAVITATION 

respect to the poles, have undergone no per- 
ceptible change from the earliest ages." 1 It 
should be remembered that the amount of the 
shifting of the axis that would be adequate to 
account for the motion of precession would be 
so small that it would be impracticable to de- 
tect it by any such test as geographical dis- 
placement. 

LXVI. 

Variable Direction of the Inluence of 
Disturbing Bodies. 

Thus far in these investigations, the influ- 
ence of the disturbing bodies has been con- 
sidered as reaching the center of the earth 
through the plane of the equator. It follows, 
then, that the precession of the equinoxes 
would exist, if the sun, moon, and planets 
moved constantly in this plane, and that, too, 
whether the earth were solid or fluid ; whether 
it had a thick or a thin solid crust ; whether 
it was spherical or had its present figure. 

If we could view the axis of the earth from 
the equinoctial point 1, Fig. 5, it would be 
situated at A, at the extremity of the dotted 
line 1, and perpendicular to it. In this posi- 

1 The second fact here referred to has been considered in 
Section XL VIII. Chap. II. 



THE DETERMINING FORCE. 97 

tion the poles are equidistant from the moon, 
and have an equal motion toward that satel- 
lite. When the influence of the moon reaches 
the center of the earth through either hemi- 
sphere, that hemisphere is partially in the 
shorter limb of the eccentric, and the opposite 
hemisphere is equally in the longer limb. 1 

LXYII. 

Axis of Rotation not Coincident with the 
Geometrical Axis. 

The inclination of the axis of the earth to 
the plane of the ecliptic, and the motion of 
the earth in its orbit, cause the influence of 
the sun and moon to reach the center of the 
earth through the northern or southern hem- 
isphere, except when they act in the line of 
the equinoxes. When they are vertical over 
the summer solstice, their influence reaches 
the center of the earth through the northern 

1 These conditions cause the ebb and flow of the tides on 
the longer limb of the eccentric at the nadir, in the opposite 
hemisphere from the disturbing body. 

The tidal forces would be rapidly decreasing in the higher 
latitudes, in consequence of the less rapid axial velocity, 
were it not that the tendency of matter to move in a given 
plane decreases with the velocity, and the points at which 
the tidal wave culminates changes its position less rapidly. 



98 GRAVITATION 

hemisphere. The south pole is then in the 
longer limb of the eccentric, and the north 
pole is in the shorter limb. 

If the influence of the sun and moon were 
removed from the earth, its path in the heav- 
ens would become rectilineal, and its axis of 
rotation would coincide with its geometrical 
axis. With a given axial velocity, the more 
rapid the deviation from a right line, the 
the greater would be the remove of the center 
of the axis of rotation from the geometrical 
center. 

LXVIII. 

Theories of Nutation. 

When the influence of the sun and moon 
reaches the center of the earth through either 
hemisphere, that hemisphere is in the short 
limb of the eccentric, and the opposite hemi- 
sphere is in the longer limb and has a more 
rapid motion toward the moon than the 
shorter. This has the effect to elevate one 
pole and depress the other, thus affecting the 
obliquity of the ecliptic. 

When the disturbing influence crosses the 
equator, the pole that was before depressed is 
now elevated, and thus is produced the mo- 
tion that is termed the nutation of the 
earth's axis. This theory of the cause of 



THE DETERMINING FORCE. 99 

tation has the advantage over that which at- 
tributes it to the influence of the sun and 
moon upon the excess of matter about the 
equator, inasmuch as the former theory as- 
signs a cause which tends at one time to in- 
crease and at another k) diminish the obliquity 
of the ecliptic ; while the latter theory, that 
of Newton, assigns a cause which tends con- 
stantly to bring the plane of the equator and 
the plane of the ecliptic into coincidence. 

The tendency of matter on the equator to 
move in a given plane, in consequence of the 
axial rotation, combines with the motion of 
nutation, and the resultant of these forces is 
a modified circuit of the poles in space. 

The sun and planets have their independ- 
ent influences, and at times they act more or 
less in unison, causing a variation of the posi- 
tion of the earth's axis, and making the poles 
of the earth to describe irregular undulating 
ellipses in the heavens, around the poles of 
the ecliptic. 

The return of the poles of the earth to 
given points in the heavens, and the return 
of the plane of the equator to a given position 
in relation to the plane of the ecliptic, de- 
pends upon the return of the sun, moon, and 
planets to a given position in the heavens, 
in relation to the center of the earth. 



100 GRAVITATION 



CHAPTER IV. 

THE SECULAR ACCELERATION OF THE MOON'S 
MEAN MOTION. 

LXIX. 
Moon's Acceleration. 
When Dr. Halley and other eminent astron- 
omers came to compare the astronomical rec- 
ords of the ancient Chaldeans and Arabians 
with modern lunar tables, they found convin- 
cing evidence that, during the intervening 
centuries, the periodic time of the moon's rev- 
olution had undergone a perceptible diminu- 
tion ; or, in other words, that there has been 
a perceptible acceleration of the moon's mean 
motion in her orbit. How to ascertain the 
physical cause of this acceleration was a prob- 
lem that greatly perplexed astronomers dur- 
ing a considerable portion of the eighteenth 
century. 

The French Academy of Sciences at Paris, 
ever zealous to advance the cause of true 
science, offered a prize in 1770, to induce a 
thorough study of this problem, and to bring 



THE DETERMINING FORCE. 101 

about, if possible, a determination of the 
question whether the acceleration could be ac- 
counted for as an effect of gravitation. Euler, 
one of the first mathematicians of the as:e, 
received the prize, although he did not reach 
a solution of the problem. He says : " There 
is not one of the equations about which any 
uncertainty prevails, and now it appears to be 
established by indisputable evidence, that the 
secular inequality in the moon's mean motion 
cannot be produced by the force, of gravita- 
tion." x Earnestly desiring a solution of this 
intricate and interesting problem, the Acad- 
emy of Sciences continued to offer its stim- 
ulating prizes. 

Euler extended his researches, and reaf- 
firmed his previous conclusion ; saying, at the 
same time, " That no doubt henceforth could 
exist that the inequality arose from the resist- 
ance of an ethereal fluid pervading the celes- 
tial regions." The resistance, it was said, 
would " lessen her centrifugal force. The 
earth woidd consequently draw the moon 
closer to herself, thus diminishing the magni- 
tude of her orbit and decreasing her periodic 
times." 

Others investigated this interesting and per- 

1 Grant's History of Astronomy, pp. 61-64. 



102 GRAVITATION 

plexing subject, and received the prize. But 
none were able to account for the acceleration 
by the theory of gravitation. 



LXX. 

Hypothesis of Laplace. 

While other scientists were thus becoming 
skeptical upon the theory of gravitation, La- 
place remained a firm and constant believer 
and advocate. He may, therefore, have felt 
that necessity was laid upon him to assign the 
physical cause of the discovered acceleration 
of the moon's orbital motion. Herschel says : 
" It was in this dilemma that Laplace once 
more stepped in to rescue astronomy from 
its reproach." And it seems that Laplace 
ended the controversy by advancing the hy- 
pothesis " that it depends on the secular varia- 
tions of the eccentricity of the earth's orbit." 
He found that "the action of the planets 
produced nothing of the kind." He traced 
the disturbance directly to the sun. 



THE DETERMINING FORCE. 103 



LXXL 

Objections to the Hypothesis of Laplace. 

But how can the sun " transmit," or, as he 
says, " reflect " back to the moon the action 
of the planets, so as to affect its periodic time, 
without affecting the periodic time of the 
earth, when the earth is a near neighbor of 
the moon ? Then, again, the orbits of the 
moon and earth are both concave toward the 
sun ; and the moon's orbit, viewed from the 
sun, dwindles almost to a point, since the di- 
ameter of this orbit is only about one half the 
diameter of the sun. 

The mean distances of the moon from the 
earth, and of the moon and earth from the 
sun, depend upon their centrifugal and centrip- 
etal forces, since the forces poise each other. 
That these forces are constant between the 
sun, moon, and earth is proved by the perma- 
nent uniformity of the periodic times of the 
earth. 

On account of the constant variation in the 
positions of the planets, any " transmitted " 
or " reflected " action from them through the 
sun would cause irregularity in the motions of 
the earth. That Laplace, then, did not assign 



104 GRAVITATION 

the true cause of the acceleration of the moon's 
mean motion, is proved by the fact that the 
force assigned does not proportionately affect 
the motion of the earth. If the power to pro- 
duce the accleration of the moon can be traced 
to the sun, according to the theory of Laplace, 
may it not be that this power is inherent in 
that body, instead of being " reflected from 
the planets ? " As the planets are poised be- 
tween the centrifugal and centripetal forces, 
if the attraction of the earth on the moon 
were decreasing in any measure, the length of 
the moon's orbit would be increasing, and its 
periodic time would be increasing also, instead 
of diminishing, as shown by the results of 
comparison. 

LXXII. 

Is the Earth's Orbit Becoming a Circle? 
The orbits of the planets are doubtless sub- 
ject to perturbations consequent upon the in- 
fluence of each upon the other, but this fact 
hardly warrants the assertion of Herschel, 
" that the eccentricity of the earth's orbit is, 
and has been, since the earliest ages, diminish- 
ing ; and this diminution will continue (there 
is little reason to doubt), till the eccentricity 
is annihilated altogether, and the earth's orbit 



THE DETERMINING FORCE. 105 

becomes a perfect circle." " The time re- 
quired for these evolutions/' Herschel says, 
" has not been calculated." This is undoubt- 
edly true. 

LXXIII. 

Moon's Acceleration not Due to Change in 
Orbit. 

Astronomers teach that the mean distances 
of the planets from the sun never change, and 
that the periodic time of revolution for a 
given mean distance is always the same, what- 
ever be the eccentricity of the orbit. Newton, 
moreover, maintains that if the orbits of the 
planets were changed to circles whose diam- 
eters were respectively equal to the transverse 
diameters of the ellipses, their periodic times 
would remain unchanged. But this change 
would increase the length of the orbits ; there- 
fore, if the periodic times should remain the 
same as before, there must be an increase of 
orbital velocity. It is evident, then, accord- 
ing to this theory, that if the earth's orbit, as 
some astronomers claim, is changing from an 
ellipse to a circle, its length is increasing ; but 
it is impossible that the resulting increase in 
the length of the moon's orbit should cause 
the acceleration of the moon's mean motion. 



106 GRAVITATION 

As the mean distance is invariably the same 
and the ellipse is shorter than the circle, the 
orbits of the planets can never become circu- 
lar orbits. 

LXXIV. 

Moon's Acceleration not Due to Ethereal. 
Kesistance. 

" Many mathematicians of more modern 
days have considered the problem and have 
reached the conclusion that there are still 
slow changes in the motion of our satellite 
which gravitation has not yet accounted 
for." * 

The secular acceleration of the moon's mean 
motion has been attributed to " the resistance 
of an ethereal fluid pervading the celestial re- 
gions." If there were any such resistance in 
space affecting the periodic time of the moon, 
the same cause must in like manner affect the 
periodic times of the earth and the other plan- 
ets. But this theory has been at times so 
strongly maintained that I shall notice it more 
particularly in a succeeding chapter. Al- 
though there are objections to all the theories 
that have been advanced to explain the secu- 
lar acceleration of the moon's motion, the fact 

1 Newcomb's Popular Astronomy, p. 99. 



THE DETERMINING FORCE. 107 

of the secular inequality has been demon- 
strated by incontestable evidence. The in- 
quiry, then, for the true cause of this phenom- 
enon becomes one of exceeding interest. 



LXXV. 

Laplace tkaces the cause of Lunar Ac- 
celeration to the Sun. 

" Laplace, with others, studied the lunar 
problem with the most scrupulous care. He 
came to a positive conclusion that the caus- 
ative influence of the lunar acceleration ema- 
nates from the sun." If he had considered 
the disturbing effect of the sun's attraction 
upon the position of the earth's axis he would 
probably have discovered the true physical 
cause. 

The facts of astronomy afford many indica- 
tions that the sun has a proper motion in 
space. According to Herschel's calculations, 
the sun is moving at the rate of 422,000 miles 
per diem. The sun, then, as well as the moon 
does not hold the same position at the end of 
the year that it had at the beginning. 



108 GRAVITATION 



LXXVI. 



Influence of the Sun and Moon on the 
Stability of the Eakth's Axis. 

In our explanation of the physical causes of 
the tides, of the precession of the equinoxes, 
and the variation of the obliquity of the eclip- 
tic, it was shown that the deviation of the earth 
from a right line, occasioned by the gravitat- 
ing force of the sun, moon, and planets, causes 
the removal of the axis of rotation from the 
position of the geometrical axis, thus giving 
an eccentric motion to the earth. The disturb- 
ing effect of the moon on the position of the 
earth's axis, when considered by itself, tends 
to maintain a limb of the eccentric of uniform 
length, invariably turned toward itself ; and 
to cause a limb of constantly varying length 
to be passing under the sun. The disturbing 
influence of the sun tends to produce similar 
results, but of less magnitude. When the 
sun acts in conjunction with the moon, the 
length of the shorter limb of the earth is di- 
minished, and the longitude of the moon is 
increased. When the sun and moon act in 
opposition, the effect is reversed. 



THE DETERMINING FORCE. 109 



LXXVII. 

The Sun's Motion an Element in the Pkob- 
lem. 

If the sun maintained a fixed position in 
the heavens, the disturbance that we have 
been considering would have been compen- 
sated at the end of the year ; for while the 
moon's motion would have been apparently 
accelerated, in one part of her orbit, it would 
have been equally retarded in another. 

In the discussion of the subject of preces- 
sion it was shown that if the moon should oc- 
cupy the same position at the end of the year 
that it had at the beginning, there would be 
no annual precession. But the longitude of 
the sun and stars is increased by the disturb- 
ing effect of the moon upon the position of 
the earth's axis, and the motion of the moon 
is accelerated by the disturbing effect of the 
sun on the same. 

The amount of acceleration of the moon's 
motion, that observation seems to have estab- 
lished, is 11" in a century. Whether the in- 
fluence of the sun and planets operating to 
disturb the position of the earth's axis is ade- 
quate to produce that acceleration, it may be 



110 GRAVITATION 

difficult to determine with accuracy, on ac- 
count of the uncertain data respecting the 
proper motion of the sun in space, and the 
complex influences of the planets. 



LXXVUL 

The Lunar Acceleration likely to Continue 
Indefinitely. 

Herschel says : " The earth's orbit will be- 
come a perfect circle, the tables will be 
turned, and the process of ultimate restora- 
tion will commence, after which it will again 
open out into an ellipse, the eccentricity will 
again increase, attain a certain moderate 
amount, and then again decrease." Accord- 
ing to this hypothesis, the acceleration of the 
moon's orbital motion will continue while the 
earth's orbit is conforming to a circle, but 
when it begins to return to the elliptical form, 
the moon's motion will be subject to a contin- 
ual retardation. 

Laplace says : " Future ages will develop 
these great inequalities, which are periodical 
like the variations of the eccentricity of the 
earth's orbit, upon which they depend." 

On the other hand, it seems more probable, 
that the moon's mean motion will continue to 



THE DETERMINING FORCE. HI 

be accelerated, as long as the sun continues to 
change his place in the heavens ; that no fu- 
ture day will witness its retardation, whatever 
variation there may be in the form of the 
earth's orbit ; and that the longitude of the 
sun and stars will continue to increase as long 
as the moon accompanies us in our passage 
through celestial space. 



112 GRAVITATION 



CHAPTER V. 

GRAVITATION IN THE SOLAR SYSTEM. 
LXXIX. 

Laws of Matter Uniform throughout the 
Solar System. 

In a previous chapter we briefly considered 
the law of density, and indicated some of its 
effects on terrestrial matter. It will now be 
assumed that the same law is applicable to all 
the bodies of the solar system. There is 
abundant evidence that matter throughout the 
universe is under the control of gravitation, 
and is subject to similar mechanical laws. 
The wonderful revelations made within a few 
years by the aid of the spectroscope furnish 
striking proof that the elements that compose 
the earth abound in bodies remote from our 
system. This strengthens the probability of 
the universal prevalence of the laws that gov- 
ern matter here. 



THE DETERMINING FORCE. 113 

LXXX. 

Forces that Determine the Moon's Path. 

In a paper read before the Academy of 
Sciences at Northampton. Professor Alexander 
said, in substance, that the center of gravity 
in the moon does not coincide with the geo- 
metrical center of the figure, but that it is 
located farther from the earth than is the 
geometrical center of the moon. He gave no 
reason for this statement. His assertion may 
have been based on the mathematical calcula- 
tions of Professor Hansen, the German astrono- 
mer, as I believe is the custom of most astron- 
omers. According to his estimate, the moon's 
geometrical center is thirty-three English miles 
nearer to us than is her center of gravity. 

I have not seen his original calculations, 
but from the tenor of the following extract 
from the book entitled " God's Glory in the 
Heavens," I think that the fallacy of his 
hypothesis rests upon his comparison of the 
motion of the moon to that of a cannon ball 
hurled from a gun through the resisting me- 
dium of the atmosphere. " In discharging a 
ball from a gun, calculation can predict the 
trajectory it will describe. But if the ball 



114 GRAVITATION 

is not equally dense on opposite sides, it will 
not pursue the same path it would do if ho- 
mogeneous. Given the difference of density, 
the curve can be laid .down ; and given the 
curve, the difference of density can be deter- 
mined." The conditions are in no wise simi- 
lar. The motion of the moon in celestial 
space is free from resistance, and depends 
solely on the centripetal and centrifugal 
forces. 

LXXXI. 

Unequal Density of the Superior and In- 
ferior Limbs of the Moon, and 
of Comets. 

It is well known that if a guinea and a 
feather be dropped at the same instant, and 
from the same height, in a vacuum, they will 
fall through equal spaces in equal times ; but 
if, the other conditions being the same, they 
are let fall in the atinosjDhere they will not 
reach the ground at the same instant. If the 
feather were attached to the guinea, then the 
portion of the guinea most remote from the 
feather would reach the ground first ; and so 
would the heavier side of a ball, when the in- 
equality in the density of the opposite sides 
is considerable. It is admitted that centrif- 



THE DETERMINING FORCE. 115 

ugal force is excited in a revolving body, and 
that it increases with the velocity when the 
periodic times are equal. The periodic times 
of the superior and inferior limbs of the moon 
must be equal in their revolution around the 
earth. As the superior limb of the moon is 
the more distant from the earth, it must move 
in a correspondingly longer orbit. The ve- 
locity and centrifugal force of the superior 
limb must therefore be greater than the 
velocity and centrifugal force of the inferior 
limb. When a mass of matter of unequal 
density, under the influence of centrifugal 
and centripetal forces, is caused to move in an 
orbit around a central body, the rarer limb 
will move in the longer orbit, and will have 
the greater velocity and centrifugal force. If 
the earth's attractive power were increased so 
as to bring the moon nearer to the earth, the 
inequality in density of the superior and in- 
ferior limbs of the moon would be increased 
thereby, as the inequality in density must in- 
crease as the distance diminishes. If the 
present inequality in the density of the nearer 
and remoter limbs should be materially in- 
creased, there would be a greater tendency of 
the lighter and the heavier limbs to separate 
from each other, and thus to elongate the 



116 GRAVITATION 

figure of the moon. This tendency of the 
lighter limb to move in a longer orbit may 
account for the occasional division of a comet 
as it is approaching the sun. In this posi- 
tion the density of the limb nearer the sun 
would be increasing faster than the density of 
the remoter, hence they might separate and 
move on in independent orbits. If there 
are comets that wander from one system to 
another, their movements are doubtless con- 
trolled by the laws already considered. If 
the various systems of the universe are mov- 
ing in space they may, at one time, be reced- 
ing from, and, at another, approaching each 
other. A comet, then, moving through the 
remoter part of its extremely elongated orbit 
might come so near another system as to be 
brought under the control of its attractive 
power. If, however, there were no power of 
gravitation outside the solar system, no comet 
could ever permanently withdraw from it. 

LXXXII. 

Illustrative Experiments. 

If we elongate a sphere of unequal density, 
so as to form an exaggerated representation 
of the figure and condition of the moon, poise 



THE DETERMINING FORCE. \YJ 

the elongated body on a pivot that reaches 
the center of gravity through the shorter di- 
ameter, and then cause the pivot to move 
rapidly in a circle whose plane is horizontal, 
we shall find that the longer and rarer limb 
of the body will move in the longer orbit. 
We suppose the body to be poised on the 
center of gravity, for the force that moves 
this point moves the whole body, and if all 
parts of the body are equally free to rotate, 
when rotation begins, the axis of rotation in- 
variably seeks the center of gravity through 
the shorter diameter. If the motion of rota- 
tion is combined with one of translation that 
holds the body in position, the axis of rota- 
tion may coincide with the longer diameter, 
as is the case with an elongated rifle pro- 
jectile. Or, again, if we support one extrem- 
ity of the axis of rotation, this axis may be 
made to coincide with the longer diameter, as 
may be seen in a rapidly revolving elongated 
top. But whether the axis of rotation coin- 
cide with a longer or shorter diameter, it will 
seek the center of gravity. This may be seen 
in the effort of a spinning top to right itself 
when tipped several degrees from a vertical 
position. If we harness a top and place the 
axis of rotation in a horizontal position, or try 



118 GRAVITATION 

the same experiment with a gyroscope, the 
effort of the axis of rotation to find the center 
of gravity through the point of support will 
tend to balance the force of gravitation, for 
the movement in either case is upward. If 
we elevate the unsupported extremity of the 
axis of rotation above a horizontal position, 
this axis will tend still more strongly to find 
the center of gravity through the point of 
support, because the weight will be thrown 
more and more nearly over the point of sup- 
port by the decreasing length of the lever, 
and the increasing power of leverage. 

Lxxxin. 

The Rarer Limb Moves in the Longer 
Orbit. 

Referring again to the case of the elongated 
sphere. If the body should be poised on the 
center of the figure, instead of on the center 
of gravity, and then the pivot should be 
moved with varying velocity in an ellipse, 
thus representing the motion and path of the 
moon, the denser limb would not move in the 
longer orbit, but would be subject to more 
frequent axial rotation, caused by the unequal 
momentum existing in the opposite limbs. 



THE DETERMINING FORCE. 119 

According to the law laid down in Chapter I. 
the density of the inferior limb of the moon 
must exceed the density of the superior, be- 
cause gravity acts with more force upon it ; 
and the density of those portions that have 
the greatest centrifugal force is diminished, 
in consequence of their being uplifted to a 
greater distance from the center of the mass. 
The rarer matter on the moon, as well as on 
the earth, moves in the longer orbit, where the 
centrifugal force is the greatest. Hence the 
air and water, if there are any, and the lighter 
material are mainly on the superior limb of 
the moon. According to the law of density, 
the center of gravity in the moon must be 
nearer the earth than the geometrical center 
of the moon is, and therefore according to the 
laws of dynamics it could not move in the 
inverted position suggested by Professor Han- 
sen ; and, again, it will follow, that if the tra- 
jectory of the moon depends primarily upon 
its unequal density, it is not governed by 
gravitation. 



120 GRAVITATION 



LXXXIV. 

The Balanced Condition of the Moon, and 
Othek Satellites. 

The distance between the sun and moon 
being far greater than the distance between 
the earth and moon, it is evident that the in- 
equality of the earth's attraction on the oppo- 
site limbs of the moon must greatly exceed 
the inequality of the sun's attraction upon 
the same portions. Hence the preponderance 
of terrestrial gravitation on the denser limb 
causes the moon to be a balanced figure ex- 
posing only its loaded or denser limb to the 
earth. 

The balanced condition of the moon ex- 
plains the singular phenomenon of the uni- 
form rotation of the satellites of the different 
planets on their axis with each revolution in 
their orbits, although the lengths of their 
orbits and the times of their revolution are 
very unequal. Laplace said : " It is well 
known that the satellites present always the 
same face toward Jupiter, as the moon does 
toward the earth." Herschel, when speaking 
of the most distant satellite of Saturn says : 
"It is presumed with much certainty that this 



THE DETERMINING FORCE. 121 

satellite revolves on its axis in the exact time 
of rotation about the primary, as we know to 
be the case with the moon, and as there is 
considerable ground for believing to be so 
with all secondaries." 

LXXXV. 

Conditions likely to Affect the Tempera- 
ture of the Moon's Surface. 

The moon is the more stable in its balanced 
position when it has its mean motion in its 
orbit, and its denser side is turned toward 
the earth and sun, as when the moon is in 
opposition to the sun. The unequal mo- 
mentum in the superior and inferior limbs of 
the moon, resulting from their unequal orbital 
motion, when taken in connection with the 
varying angular position of the sun and its 
unequal gravitating influence on the opposite 
limbs of the moon, causes the oscillations 
termed librations in latitude and in longitude, 
as the moon is balanced toward the center 
of the earth, and its path departs from the 
plane of the ecliptic. As the moon's orbit 
maintains an angle with the plane of the 
ecliptic of about 5°, and the heavier limb of 
the moon is turned toward the center of the 



122 GRAVITATION 

earth, it is evident that the axis of the moon 
is inclined to the plane of the ecliptic, and 
that this must determine the lunar seasons. 

Some scientists have concluded that there 
must be great extremes of heat and cold on 
the surface of the moon, because the duration 
of a single day and night must equal one of 
our months. But to determine the heating 
effect of the sun's rays upon the surface of 
one of the planets, or of the moon, we must 
take into account all the known conditions 
that modify such effect. We know that the 
heating power of these rays depends very 
much upon the density of the matter upon 
which tfcey fall. Note, on the one hand, 
their effe3t upon the rare atmosphere on the 
summit of a lofty mountain ; and, on the 
other hand, their, effect upon the denser air of 
the valley. While the former may be in per- 
petual frost, it may look down upon the latter 
basking in the genial warmth of a tropical 
clime. The denser and the rarer matter have 
each their special capacities for heat, a fact 
that is turned to practical account in the arti- 
ficial formation of ice. Because the matter 
of the moon is much rarer than that of the 
earth, the greater length of the lunar day and 
night would produce much less variation in 



THE DETERMINING FORCE. 123 

temperature than a similar cause would do 
under the conditions with which we are fa- 
miliar. 

At the annual meeting of the American 
Association in 1857, Professor Henry of the 
Smithsonian Institution, read a paper prepared 
by Mrs. Eunice Foote, giving the results of 
some interesting experiments that confirm the 
positions we have taken. " Mrs. Foote took 
two glass cylinders of the same size, contain- 
ing thermometers. Into one the air was con- 
densed, and from the other it was exhausted. 
When they were of the same temperature, the 
cylinders were placed side by side in the sun, 
the thermometers in the condensed air rose 
more than twenty degrees higher than those 
in the rarefied air. This effect of rarefaction 
must contribute to produce the feebleness of 
heating power in the sun's rays on the sum- 
mits of lofty mountains. Secondly, the effect 
of the sun's rays is greater in moist than in 
dry air. In one cylinder the air was saturated 
with moisture, in the other dried with chloride 
of lime ; both were placed in the sun, and a 
difference of about twelve degrees was ob- 
served. This high temperature of sunshine in 
moist air is frequently noticed ; for instance, in 
the intervals between summer showers. The 



124 GRAVITATION 

isothermal lines on the earth's surface are 
doubtless affected by the moisture of the air 
giving power to the sun, as well as by the 
temperature of the ocean yielding the mois- 
ture. Thirdly, a high effect of the sun's rays 
is produced in carbonic acid gas. One re- 
ceiver being filled with carbonic acid, the 
other with common air, the temperature of the 
gas in the sun was raised twenty degrees above 
that of the air. The receiver containing the 
gas became sensibly hotter than the other, and 
was much longer in cooling. An atmosphere 
of that gas would give to our earth a much 
higher temperature ; and if there once was, 
as some suppose, a larger proportion of that 
gas in the air, an increased temperature must 
have accompanied it, both from the nature of 
the gas and the increased density of the at- 
mosphere." l 

LXXXVI. 

Laws Determining Magnitude of Melted 
Nucleus. 

By the application of the laws that were 
cited in the First Chapter, it becomes evident 
that the magnitude of the melted nucleus of 
the earth would be enlarged ; the density and 

1 Annual of Scientific Discovery, 1857, pp. 159, 1G0. 



THE DETERMINING FORCE. 125 

conductivity of the crust would be increased ; 
its thickness would be reduced, and the sur- 
face temperature raised, if the force of gravi- 
tation should be intensified, and vice versa. 
This law is applicable to all the bodies of 
the solar system, and shows that the density 
of a portion of the melted nucleus of all the 
planets must be the same, and that their sur- 
face temperature does not depend upon their 
distances from the sun. 



LXXXVIL 

Varying Density of the Planets. 
The decrease in the density of the planets 
as the force of gravitation affecting them de- 
creases indicates a homogeneous substance. 
Their density and physical condition are 
determined by the force of gravitation, but 
the ratio between their density and distance 
from the sun is not uniform, since the force 
of gravitation varies with their mass, figure, 
and distance of the surface from the center, 
because of their unequal magnitudes, surface 
temperature, and gravitating influence of 
each on the other (as the influence of the 
moon on the earth), as well as their distances 
from the sun. 



126 GRAVITATION 

If any of the bodies are so comparatively 
light ; or if gravitation has received so little 
resistance that they have not been melted, 
their chemical forces have not been expended ; 
they are not reduced to the condition of a 
cinder. The density of the gases depends 
on the force of gravitation ; but if we con- 
dense them to a fluid state, chemical action 
takes place. The density, however, would 
still be influenced by gravitation. If any of 
the asteroids prove to be more dense than the 
general laws of density would assign to plan- 
ets of their respective size, such a condition 
would indicate that they once were united in 
a larger body ; or, in other words, that these 
asteroids originally formed a single planet, 
and that the action of gravity, the suspension 
of which had caused the separation, had been 
reapplied to the fragments. Such a catas- 
trophe as we have here supposed might ac- 
count for the meteoric matter that from time 
to time reaches the earth. 

If we could transport a shaft of granite, a 
mile in length, from the earth to the sun, its 
weight, according to the tables, would be in- 
creased twenty-eight times. If we were to 
place it on the body of the sun, it would be 
increased more than twice that amount. But 



THE DETERMINING FORCE. 127 

as it is impossible to determine how much 
matter there may be in a state of great rare- 
faction above the body of the sun, I will 
assume that the weight of the granite is only 
doubled by its transfer from the surface to 
the body of the sun. Our granite shaft then 
becomes equal to a similar one fifty-six miles 
in length on the surface of the earth. 

LXXXVIIL 

Spots and Faculje on the Sun's Sukface. 

The general brightness of the sun indicates 
that the surface is near the line of perfect 
condensation, and that spots are dimmed only 
at points and places least under the condens- 
ing influence of gravitation, as on the equator. 
These spots may be partially refrigerated 
islands of matter floating on a fluid sea. 
Their appearance may be due to the fact that 
the planets are at a greater distance than 
usual, or that the limb of the sun on which 
these spots appear is turned away from the 
planets. The surface of the sun is brightest 
when the above conditions are reversed. 

The spots may begin to form on the 
equator of the sun, but become more visible 
as they are floating off. That they are float- 



128 GRAVITATION 

ing on the body of the sun is indicated by 
their depressed condition. The outer envelope 
of the sun is, as it were, a very dense blaze. 
The illuminated gas overhanging the edge of 
the spots may, in a measure, illuminate them, 
producing the penumbra. This view is con- 
firmed by the disappearance of the penumbra 
at the point of contact when two or more con- 
tiguous spots intercept the light. 

The faculse may be caused by the accumu- 
lation of floating specks in clusters, through 
the influence of their mutual attraction, and, 
by sweeping the surface, they may occasion 
the increased brightness of the surrounding 
surface that is apparent just before the forma- 
tion of a visible spot. When the edge of a 
spot begins to liquefy, it may begin to grow 
brighter, and complete liquefaction may cause 
greatly increased brightness, and produce the 
more or less elevated protuberances. The 
surface of a fluid sphere of unequal tempera- 
ture is always in motion. Some of the par- 
ticles are carried forward and some backward. 
This may account for the incongruities in the 
axial rotation of the different zones of the 
sun. 

As a great increase of density results in a 
corresponding increase of temperature, and a 



THE DETERMINING FORCE. 129 

degree of intensity is caused by continued 
condensation that renders matter radiant, the 
matter of the sun must be luminous. As 
the temperature of a stratum depends upon its 
density, the light of the sun must be as per- 
manent as gravitation. 

LXXXIX. 

The Sun not Deteriorating. 

The destruction of the matter of the sun has 
been discussed by many scientists, and some 
have made elaborate calculations to show what 
the annual waste must be, yet matter is inde- 
structible. The constancy in the periodic time 
of the earth shows that gravitation is con- 
stant ; this gives the temperature which causes 
the vibration, a ray, or sunbeam, converted 
into heat when resisted. If we can count on 
gravitation as ever acting and never wasting, 
we can with equal confidence conclude that 
the sun is not subject to deterioration. Some 
maintain that the heavenly bodies are cooling 
off and that the smaller are the colder. That 
being the case, the darker planets would be 
growing hot, since they could not radiate heat 
from their dark surfaces as rapidly as they 
would be receiving it from the ever-glowing 



130 GRAVITATION 

sun. This process would go on until all the 
bodies of the solar system were nearly of the 
same temperature, and then they would cool 
off together. But when they should all have 
entered their icy tomb, where should we look 
for all this heat ? Surely not in space, for in 
that there is no matter, no resistance, and 
therefore no heat. 

XC. 

Thickness of Crust of the Earth, Jupiter, 
and of the moon. 

If we are correct in our conclusion that the 
body of the sun is a mass of perfectly con- 
densed matter, and that it is kept in this con- 
dition by the force of gravity, we are furnished 
with data that will enable us to determine, 
approximately at least, the thickness of the 
earth's crust. We have seen that were a shaft 
of granite one mile in length to be transferred 
to the body of the sun, its weight would be 
increased fifty-six times, or, in other words, it 
would be equivalent to a similar shaft at the 
surface of the earth fifty-six miles in length. 
So, then, if we could descend through a com- 
paratively thin crust, and then through molten 
matter increasing in density until we had 
reached the depth of about fifty-six miles, — 



THE DETERMINING FORCE. 131 

making no allowance for loss of weight as we 
descend, — we should arrive at a perfectly 
condensed nucleus having the same density 
and temperature as the sun. 

According to the calculations of Professor 
Proctor, the force of gravity on the surface of 
Jupiter is about seven times as great as it is 
on the surface of the earth. Therefore, by 
the application of the same law that gave us 
the distance to the perfectly condensed nu- 
cleus of the earth, we should reach the cor- 
responding nucleus of Jupiter at the depth of 
about eight miles. 

As the force of gravity at the surface of 
the moon is about one sixth of what it is at 
the surface of the earth, making no allowance 
for loss of weight as we descend below the 
surface of the moon, we should have to go 
to the depth of about 336 miles, before we 
should reach the perfectly condensed nucleus. 

If we should find it necessary to limit the 
solid crust of the earth to the thickness of 
twenty-eight miles, the application of the uni- 
form law would make the thickness of the 
solid crust of Jupiter but four miles, one 
seventh that of the earth, as in the former 
case. By the same law the moon's crust 
would be 168 miles in thickness. If the crust 



132 GRAVITATION 

of the earth is 21 miles in thickness, the 
crust of Jupiter may be 3 miles in thickness, 
and that of the moon 126 miles. If the crust 
of the earth should prove to be no more than 
14 miles in thickness, that of Jupiter would 
be about 2 miles, and that of the moon about 
84 miles. On the surface of the earth a col- 
umn of granite about three miles high would 
have its base crushed by the superincumbent 
weight. The loss of weight consequent upon 
the descent below the earth's surface, and the 
increase of sustaining strength must be taken 
into account in estimating the thickness of 
the crust. Making due allowance for these 
modifying causes, it seems probable that the 
earth's crust is less than 14 miles in thick- 
ness. It may seem that the increase of tem- 
perature as we descend into the earth is not 
sufficiently rapid to warrant the above conclu- 
sion, but it should be noted that at the point 
where granite is crushed the temperature in- 
creases rapidly. 

The crust of the moon must be thick and 
rare, with a low conducting power, and low 
mean surface temperature as compared with 
the earth. 

As the unequal refrigeration and contrac- 
tion of the interior and exterior portions of 



THE DETERMINING FORCE. 133 

the earth's crust caused the inequalities on its 
surface, and as rare matter contracts more in 
the process of refrigeration, the formation 
and contraction of a rare and thick crust must 
cause great surface inequalities, such as the 
appearance of the moon's disk indicates. 

XCI. 

Location of the Gkeatest Inequalities. 

The crust of the earth is the lightest, as 
well as the rarest and thickest, at the equator. 
The greatest surface inequalities are therefore 
found in the warmer climates, as seen in the 
altitude of table lands and mountain ranges. 
The crust being most elevated, rarest, and 
lightest where it is least affected by gravita- 
tion, the greater altitudes, and more than one 
half of the land, are located in the northern 
hemisphere. This condition accords with the 
fact that the inclination of the earth on its 
axis, and the motion in its orbit, causes the 
south pole to approach nearer to the sun than 
does the north pole, subjecting it to more 
powerful attraction, since the inequality in the 
influence of the sun on the opposite limbs of 
the earth increases as the distance between the 
sun and each of them decreases. It is true 



134 GRAVITATION 

that the variation of the force of gravitation in 
the two hemispheres is exceedingly slight, but 
it is also true that the variation in altitudes is 
very small when compared with the thickness 
of the crust. 



XCII. 
Motion of the Line of the Apsides. 

As the line of the apsides of the earth 
makes an entire revolution in about 115,000 
years, as calculated by some astronomers, and 
the uplifts and depressions on the surface are 
very gradually changing their position, the 
time may come when the excess of land in the 
northern hemisphere will be transferred to the 
southern. 

It is known that the sun has a translating 
motion in space, and that the earth in going 
round the sun is seven or eight days longer in 
advancing from the vernal to the autumnal 
equinox than from the autumnal to the ver- 
nal. So the sun moves further in its orbit 
while passing through the longer of these 
periods than while passing the shorter, thus 
causing the line of the apsides to have a very 
slow rotating motion in space. And by the 
application of Kepler's first law, we see that 



THE DETERMINING FORCE. 135 

all the heavenly bodies move in elliptical orbits 
having the attractive body in one of the foci. 
Hence they do not have a uniform motion in 
their orbits. This fact together with the mo- 
tion of the sun must keep their nodes as well 
as the line of their apsides in motion. 



xcm. 

EXTEKIOR AND INTERIOR CONDITION OF JUPITER. 

From statements already made, it is evident 
that were a shaft of the earth's crust, the 
height of which should represent the thick- 
ness of that crust, to be transported to the 
planet Jupiter, the weight of the shaft would 
be about seven times what it was before. Now, 
had the shaft been originally congealed on 
that planet, its density and conductivity would 
have been increased ; hence it follows that the 
melted nucleus of Jupiter must be compar- 
atively large, its crust dense and thin, with a 
great conducting power that keeps the surface 
at a high temperature. As the expansive 
force of heat is most apparent in matter that 
is least affected by gravitation, the high sur- 
face temperature would inevitably convert the 
surface liquids of Jupiter into a vapory envel- 
ope surrounding the planet, thus making it a 



136 GRAVITATION 

comparatively rare body when taken as a 
whole, that is, as a sphere whose diameter is 
limited by the outer surface of this envelope. 
This high surface temperature greatly expands 
the outer envelope of the sun, and of the 
other larger planets, as well as that of Jupiter. 
The same surface expansion may be percepti- 
ble in some of the comets as they approach 
the sun. As dense matter contracts less in 
congealing, a thin dense crust like that of 
Jupiter would give but slight inequalities. 

XCIV. 

Condition of the Planetary Envelopes. 

The loss of gravity must cause the outer 
portion of the envelope of vapor to be very 
rare, with a correspondingly reduced tempera- 
ture, as is the case with the upper regions of 
our own atmosphere. At a low temperature, 
the reflective power of vapor is greatly in- 
creased, and far exceeds that of land and 
water. That this is the condition of the outer 
envelopes of some of the larger planets is in- 
dicated by their great reflective power, as well 
as by their variable surfaces. 



THE DETERMINING FORCE. 137 



xcv. 

Geological and Meteorological Phenomena 
upon Jupiter and Saturn. 

From the consideration of the crushing 
force of gravity at the surface of Jupiter, we 
have seen that the solid crust of this planet 
may be no more than one mile and a half in 
thickness. The melted nucleus must be very 
large when compared with that of the earth ; 
its crust dense and thin, with high conducting 
power, maintaining the surface at a high tem- 
perature. It is probable that all the larger 
planets are in a similar condition. When 
fluids are very sensibly elevated by centrifugal 
force, as is the case on the larger planets, 
they will form more or less in ridges parallel 
with the plane of their rotation. This is very 
easily demonstrated. Light reflected from 
deep ravines and elevated ridges would cause 
the surface to have the appearance of varie- 
gated belts, and ridges formed of vapor must 
undergo frequent changes by condensation. 
The physical disturbing forces on these plan- 
ets must have great energy. This will ac- 
count for the violent storms that astronomers 
have recently observed to be raging on these 



138 GRAVITATION 

bodies. The disturbance is caused in part by 
the rapid evaporation and condensation, which 
would give unceasing activity to the leveling 
forces 5 and in part, by the rapid motion on 
their axes, aided by the mass and unequal 
revolutions of their moons, causing great in- 
stability to the planet's axis of rotation ; for the 
more they act in unison the farther they carry 
the axis of rotation from the position of the 
geometrical axis, thus keeping up, more or 
less constantly, a vibration of the axis. Then, 
too, we are to take into account the unequal 
masses of the moons of Jupiter accompanied 
by fluctuations in the tidal waves, causing 
eight tides in every term of ten hours, contin- 
ually varying from higher to lower, as the 
moons act more or less in unison. Changes, 
and active forces like these, in connection with 
the nearness of the fluid nucleus to the sur- 
face, would necessarily cause volcanic action 
on a grand and extensive scale. The immense 
volumes of dark and heated vapor that ascend 
at times would reduce the reflective power of 
the vapor overhanging a very large extent of 
surface. At other times, eruptions would 
cover vast tracts with molten matter. The 
heat ascending from such extensive fields of 
melted lava would, in some degree, disperse 



THE DETERMINING FORCE. 139 

and illuminate the superincumbent vapor. 
The appearance that we should naturally be 
led to expect from such action accords very 
well with the description of the pinky hues 
recently observed by astronomers. These con- 
vulsions may cause the more permanent spots 
on the disk of Jupiter ; those which do not 
disappear with a reconstruction of the belts. 
After spots make their first appearance, it has 
been noticed that their velocity increases, for 
a while, with each successive rotation. As the 
ascending vapor leaves the body of the planet, 
its velocity is much less rapid than that of the 
outer envelope which it is penetrating, hence 
the proper motion of the spots is constantly 
increasing until they acquire the velocity of 
the outer envelope. 

In an article published in u Harper's New 
Monthly Magazine" for March, 1882, it is 
stated that " Professor Hall on the 7th of De- 
cember, 1876 saw a bright spot upon Saturn's 
equator. It elongated itself from day to day. 
Such a thing had never before been known 
upon this planet, and had it not been that 
Professor Hall was engaged in observations 
upon the satellites, it would not have been 
seen then." 

I am of the opinion that the bright spot on 



140 GRAVITATION 

the surface of Saturn seen by Professor Hall 
was the eruption of a volcano of molten mat- 
ter that advanced from day to day down the 
side of the volcanic mountain. 



XCVI. 

Heat Kadiated from the Earth does not 
pass the Limits of the Atmosphere. 

Those who have advocated the original 
fluidity of the earth have maintained that the 
surface heat has disappeared in space, by radi- 
ation, or otherwise, instead of being central- 
ized by conduction. It may be that heat ra- 
diates from the surface of the earth, but we 
have no evidence that it passes the bounds of 
the atmosphere. Nature seems to have pro- 
vided an effective barrier against its escape, 
by saturating the atmosphere with watery 
vapor, a most active absorbent of radiant 
heat. If any heat should get beyond the 
vapor-saturated portion of the atmosphere, it 
would encounter a rare atmosphere of low 
temperature, that would expand by the slight- 
est application of heat, and thus the latter 
would be converted into force before reaching 
the outer limits of the atmosphere, and what- 
ever conduction there might be would be in 



THE DETERMINING FORCE. 141 

the opposite direction toward the denser mat- 
ter. 

When the surface of the earth was at a 
fluid temperature, the radiating force was cor- 
respondingly intense, but at that primitive 
period, all the water was held in suspense, 
forming a vapory envelope that effectually 
prevented the escape of heat. Neither could 
heat be conveyed away from the earth by con- 
duction, for in celestial space there is no ap- 
preciable matter, as will be shown in the final 
chapter. 

The power emanating from the sun is de- 
veloped into the quickening influence of heat 
and light only as it impinges on the atmos- 
phere, or on the body of the planet; the 
denser the matter on which it impinges the 
more sensible is the heat. The resistance that 
condensed nebulous matter originally offered 
to gravitation caused the solar system to as- 
sume a molten condition ; and if the force of 
gravitation should be withdrawn, the matter 
of which the system is composed would return 
to its primeval condition. 



142 GRA VITA TION 



CHAPTER VI. 

PRINCIPLES OF PLANETARY, MOTION AND 
ETHEREAL RESISTANCE. 

XCVIL 
Theoeies of Resistance to Planetary Motion. 

Sir Isaac Newton maintained that any 
ether, however subtle, would act as a retarding 
medium ; and since Newton's day there have 
been some who were ever ready to attribute 
any inequality in the motions of the planets 
to the resistance of an ethereal fluid in celes- 
tial space. 

Some of the advocates of the vibratory ethe- 
real propagation of light have affirmed that 
the resistance of this medium to planetary 
motion has diminished the magnitude of the 
moon's orbit, and caused an acceleration of 
the mean motion of this satellite. Others have 
compared the trajectory of the moon to that 
of a ball projected from a gun through the 
atmosphere. In the " Principia," Book III. 
Prop. 42, Newton says : " Bodies may, in- 
deed, persevere in their orbits by the mere 



THE DETERMINING FORCE. 143 

laws of gravity, yet they could by no means 
have at first derived the regular position of 
the orbits themselves from those laws." I be- 
lieve that this view is generally adopted. 
Robinson says : " We perceive that the eccen- 
tricity of orbits, and mean distances from the 
sun, depend on the amount and direction of 
the original impulse or velocity which the 
planets have in some way obtained, and it is 
not necessary that the planets should have any 
definite impulse, either in amount or direction, 
if the direction is not directly to or from the 
sun." 

In this chapter the attention of the reader 
will be invited to some remarks upon the laws 
of planetary motion, and I shall endeavor to 
establish the improbability that there is any 
resisting medium in celestial space, and also 
to show that the simple force of gravitation 
may have been the primitive cause of planetary 
motion. 

XCVIII. 

The Eixg Hypothesis of Laplace. 

Newton stated that if a ball could be pro- 
jected in a horizontal direction, from an alti- 
tude that would clear every mountain range, 
and with a velocity sufficient to poise gravita- 



144 GRAVITATION 

tion, and cause the ball to describe an orbit 
around the earth, it would without any ad- 
ditional impulse continue to revolve in that 
orbit. 

He further maintained that if a body, when 
projected in free space, is exposed to the ac- 
tion of a central force, varying inversely as 
the square of the distance, it would revolve in 
an orbit which would be one of the conic sec- 
tions. 

That Laplace believed in a primitive im- 
pulse transverse to the direction of gravity is 
evident from the following statement quoted 
from him. " The inertia of matter is most 
remarkable in the motions of the heavenly 
bodies, which, during a great many ages, have 
not suffered any sensible alteration." He fa- 
vored the theory that the nebulous matter 
originally existing in space and extending far 
beyond the orbit of Neptune, after it had 
been condensed into a rotating spheroid, by 
its centrifugal force threw off successive rings 
of matter, as the rotation became accelerated 
in consequence of gradual condensation. The 
rings being sustained in their elevated posi- 
tions by the centrifugal force that uplifted 
them, and by some cause becoming ruptured, 
the several portions contracted upon them- 



THE DETERMINING FORCE. 145 

selves, assumed a spherical form, and thus 
formed planets. According to this theory the 
original rotating velocity of the rings gave the 
planets their primitive impulse transverse to 
the force of gravitation, or, in other words, 
gave them their centrifugal force. 

But if the nebulous matter composing the 
solar system were condensed into a single ro- 
tating spheroid, there would be no foreign 
matter in the solar system to cause any resist- 
ance or axial disturbance. Now if the above 
theory were correct, the axes of the uplifted 
rotating rings would be parallel with the axis 
of the central rotating mass. It would follow, 
then, that the axes of the planets would be 
parallel with each other, and also perpendicu- 
lar to the plane of the ecliptic ; but, on the 
contrary, some of them are greatly inclined. 
In the case of Venus, the inclination is found 
to be about 75°. 

As the rings uplifted by centrifugal force 
would have been circular, the orbits of the 
planets would have been circles instead of 
ellipses as required by Kepler's first law. If 
they were originally hurled into space from a 
single rotating spheroid, their orbits should be 
parallel in a given plane instead of varying, 
as they do, more than 34°, and in the case of 
some of the satellites^ more than 78°. 



146 GRAVITATION 

One of the most important statements by 
which Laplace substantiates his genetic theory 
is this : " The planets rotate in a direction 
the same as that in which they go round the 
sun, and on axes approximately perpendicular 
to their orbits." Since Laplace wrote this, 
it has been contradicted, first in relation to 
Uranus, and more recently in relation to Nep- 
tune. 

XCIX. 

Facts Inconsistent with the King Hypothesis. 

According to this theory, when the superior 
rings were thrown off, they must have been 
of enormous circumference, then there must 
have been a gradual decrease down to the in- 
nermost rings. It seems highly improbable 
that an uplifted ring should contain the vast 
amount of matter found in Jupiter and its 
moons, the next suffice only to form the aste- 
roids, and the one next below contain matter 
enough to form our earth and its accompany- 
ing satellite. The asteroids, unless they are 
the parts of an exploded planet, must have 
been formed of independent rings, as they 
must have been uplifted in circles. Each ring, 
whether it had been subject to a fracture in 
one place, or in several places, must have con- 



THE DETERMINING FORCE. 147 

tracted upon itself, and thus have formed a 
single mass. If the rings of Saturn were up- 
lifted from the body of the planet, they must 
be uniform in density and distance from the 
planet, through their entire circumference, 
for the matter could not have been uplifted 
unless it were free to move ; and centrifugal 
force would not have thrown up matter in 
this condition, that was not uniform in den- 
sity. The stability, in their orbits, of Saturn's 
rings indicates that the elements do not an- 
swer the conditions necessary for the ring hy- 
pothesis. 



Axial Rotation not Explained by the Ring 
Hypothesis. 

If the orbits of some of the satellites ap- 
proach so nearly to circles that their orbital 
motion might be explained by the ring hy- 
pothesis, their axial rotation is inconsistent 
with it, for it is said that the unequal rotating 
velocity of the inner and outer portions of the 
rings gave the planets their axial rotation. 
If so, a similar motion must have been im- 
parted to the satellites, but when we consider 
their unequal masses, and the axial rotation 
which must have been imparted, in accordance 



148 GRAVITATION 

with the ring hypothesis, it does not agree 
with their actual rotation which is caused by 
their balanced condition. Kepler's first law 
demonstrates that the matter of which the 
planets are formed could never have moved 
in circular orbits ; and comets traverse indif- 
ferently almost every part of the heavens. 

The fallacy of the ring hypothesis is evi- 
dent when we compare the rotating velocity 
of the equator of the central mass with the 
orbital velocity of the nearer satellite. For 
instance, by the ring hypothesis, when the 
ring or planet Mercury was thrown off, the 
sun must have filled the orbit of Mercury, 
and its equatorial axial velocity must have 
agreed with the orbital velocity of that planet, 
which is nearly 110,000 miles per hour. 
Then, as the sun must have contracted, its ro- 
tating velocity must have proportionately in- 
creased ; and centrifugal force increases with 
the increase of velocity, and the diminution 
of the periodic time ; but instead of such in- 
creased velocity, which would have caused the 
surface of the sun to fly off into space, the 
equator of the sun has a velocity of only 
about 4,500 miles per hour. 



THE DETERMINING FORCE. 149 

CI. 

Significance of Recent Discoveries, etc. 

The fallacy of the ring hypothesis has re- 
ceived another demonstration by the discov- 
eries that have been made in relation to the 
moons o£ the planet Mars. It has been found 
that the interior satellite travels around the 
primary a little more than three times while 
the primary is making a single revolution on 
its axis. It is impossible that the ring hy- 
pothesis should account for this result. In 
fact all the planets may be moving in their 
orbits too rapidly to allow the supposition that 
they were ever attached to the body of the 
sun. 

Newton taught, and the same is presented 
in our text-books generally, that an impulse 
in a direction parallel to the horizon would 
be necessary to project a body from the earth 
and cause it to "go on revolving through 
the heavens " in a trajectory like that of the 
moon's orbit, since the body would have a 
translating velocity equal to that of the earth. 
To account for the existing facts on this basis 
it would be necessary to suppose the direct 
application of an independent force to each 



150 GRAVITATION 

planet in a direction tangential to the sur- 
face of the sun, and to each satellite tangential 
to the surface of its primary. Not only is 
such a theory at variance with the known 
methods of nature, but a simpler one will bet- 
ter account for the facts that require explana- 
tion. 

As gravitation was an active force in the 
beginning, solar motion was coeval with it. 
Planetary matter, which was distributed 
through space, must have been grouped into 
independent rotating bodies, as is indicated 
by the form and orbital velocity of the sev- 
eral planets and satellites. 

When we consider the operation of the 
force of gravitation in connection with the 
proper motion of the solar system in space, it 
becomes evident that the matter of which the 
bodies belonging to this system are composed 
could never have formed a single coherent 
mass, as is maintained by the ring hypothesis 
of Laplace. 

CII. 

Initial Effects of Gravitation. 

When gravitation was first imparted to the 
matter of the solar system, every particle be- 
gan to be drawn toward every other particle ; 



THE DETERMINING FORCE. 151 

this must result in motion in the direction of 
the greater force. All particles, therefore, 
would be set in motion, each falling toward 
every other, except the more central portions, 
which would have a more or less balanced po- 
sition by reason of the opposite attractive 
force of the surrounding matter. Then, too, 
all the matter of this system would be moving 
in obedience to the attractive force of matter 
beyond its own limits. Its different portions 
would be moving with unequal translating ve- 
locities, in accordance with the law that the 
force of gravity varies in intensity inversely 
as the square of the distance. 

If the force of gravitation were confined to 
the matter of the solar system, and this sys- 
tem were at rest in space, the tendency would 
be for all the particles to fall toward the 
center, and become consolidated into a single 
sphere. But as soon as this nebulous mass is 
subjected to the attractive force of a mass 
whose center is very remote, all the conditions 
are changed. The motion of the particles of 
the solar system is no longer in straight lines 
toward its own center, for that center is in 
motion, and the combination of the two is a 
curvilinear motion of the particles. The ten- 
dency would still be for all the matter within 



152 GRAVITATION 

a considerable central segment parallel to the 
direction of translating motion of the solar sys- 
tem to accumulate in a central mass; and 
a considerable portion of these particles would 
strike the growing mass on a line with the 
motion of translation without any tendency to 
axial rotation. Others falling more or less 
on a tangent would thereby generate a com- 
paratively slow axial motion. 

Other segments of this nebulous matter out- 
side the central segment already considered, 
while sharing in the translating motion of the 
entire system, would be unequally affected by 
it, some portions moving faster, and some 
slower, according to the varying force of 
gravitation. These particles tending toward 
each other, at the same time that they are 
drawn toward the center of the system, tend to 
form new masses moving with velocities vary- 
ing according to their respective distances and 
positions from the center, those that are car- 
ried forward faster than the center fall before 
it, while those that move slower than the cen- 
ter fall behind, thus producing the circular or 
spiral motion as seen in the action of the 
water, Fig. 2. 

Axial rotation would be produced in each 
of these new masses, or spheres, in the same 



THE DETERMINING FORCE. 153 

way we have shown that it would be pro- 
duced in the case of the central sun, except 
that in the latter instance the larger the accu- 
mulating mass the more rapid the axial rota- 
tion. Then, too, since the masses would con- 
serve both the motion of falling toward the 
center of the system and the motion of trans- 
lation which the particles had before they 
cohered, the path of the mass must be curvi- 
linear toward the central body. Under these 
circumstances, as the centrifugal force would 
increase, by reason of the increasing velocity, 
more rapidly than the force of gravity in- 
creases, on account of diminishing distance, 
hence the planet would depart from the cen- 
ter of motion, the centrifugal force would 
then be counteracted by the decreasing velo- 
city and the centripetal force, until the latter 
should gain the supremacy, and then the 
planet would begin again to approach the cen- 
ter of its motion. The cyclic variation and 
poising of these two forces compel each new 
planet to move in an elliptic orbit. 

It is evident that every newly-formed planet 
would itself become a reservoir of attractive 
power, and thus tend to become a new center 
for any lesser accumulation of matter that 
might come within the sphere of its special 



154 GRAVITATION 

control ; thus the orbit of a secondary would 
be determined. 

The matter in the segments of the solar 
system remote from the central segment 
would naturally consolidate later than the cen- 
tral portions, and in larger masses ; and as the 
elements would be subject to less intensity of 
the acting forces, they would have less density 
of structure. All this seems to be in har- 
mony with existing facts as revealed by astro- 
nomical observation. 



cm. 

Beginning of Orbital Motion. 

As the density of matter depends in a great 
measure on its volume, the unequal mass and 
density of the accumulating bodies gave un- 
equal density to the opposite jDortions of the 
concentrating mass, as is seen in the motion 
of the satellites, and as may have been the 
case with the rings of Saturn. Aside from 
the central mass, the smaller the body the 
less is the original tendency to an axial rota- 
tion ; and the nearer the satellites are to the 
primary, the more unequal is gravitation on 
the opposite limbs. Thus the denser limbs of 
the satellites were originally poised toward 



THE DETERMINING FORCE. 155 

the primaries. We have then good reason 
to conclude that the direct force of gravita- 
tion was the genetic impulse in the formation 
of the solar system, and that in obedience to 
it homogeneous nebulous matter originally fell 
from a state of rest, and finally formed in 
masses, or in rings, as in the system of Sat- 
urn. 

We see that these masses originally fell by 
centripetal force, with accelerated velocity, 
from unequal altitudes toward two common 
centers, until arrested by centrifugal force, 
which stayed the downward progress and 
hurled them off from their centers, causing 
the orbits of the planets to be more or less 
elliptical, according to the original position of 
the matter, and the central body to be located 
in one of the foci of this elliptical orbit. 

CIV. 

Composition or Fokces. 

The centripetal force and the velocity in- 
crease as the distance between the bodies is 
diminished ; and centrifugal force increases 
with the increased velocity of the bodies, or 
diminished circumference of the orbit. Hence, 
the nearer the body to the primary, the more 



156 GRAVITATION 

rapid is its orbital velocity, and vice versa, 
causing the radius-vector to describe equal 
areas in equal times. 

Gravitation, or centripetal force, is contin- 
ually tending to bring the secondaries to the 
primaries, and centrifugal force is continually 
driving them away. The unequal translating 
velocities of the planets in the different por- 
tions of their orbits depend upon the compo- 
sition of these forces, instead of upon any in- 
ertia, or any special impulse that may have 
been imparted to them at creation. This is 
indicated by the motion of comets. As they 
recede from the sun their motion becomes 
sluggish, and some of them come nearly to a 
stand-still, their centrifugal force being at this 
point nearly counteracted by the gravitating 
force of the sun. In the early genetic day 
of creation, when the particles first formed 
in clusters, some of them may have traveled 
in different directions in space. But as there 
is a tendency to rotate in a given direction, 
they were mainly hurled in that direction, as 
is seen in the motion of the planets, and as 
has been the case with any retrograde matter 
or comet that has in any way been entangled 
with the planets. The union would by add- 
ing weight permanently increase the density 



THE DETERMINING FORCE. 157 

and surface temperature, the angle of inci- 
dence in impact would determine its effect on 
the axial rotation. 

If the resultant of the translating velocities 
of these bodies that have been gathered into 
the controlling sphere of attraction of any 
planet is less than the velocity of the planet 
itself, the planet would fall nearer the sun ; 
the centripetal and centrifugal forces would 
be increased ; this would increase the velocity 
and diminish the periodic times of the planet. 
This may account for the fact that the plan- 
ets are generally nearer the sun than the 
comets are, and that the orbits of the former 
are more nearly circular. 

The remoter matter that did not coalesce 
and move in obedience to the general ten- 
dency probably took shape in some of the 
comets, and in the moons of Uranus and Nep- 
tune. 

When the planets first took their form, they 
may have moved more or less in a transverse 
direction from the present plane of their or- 
bits, but as they gravitated in a transverse di- 
rection from the action of the centripetal and 
centrifugal forces, the orbits of the planets 
and satellites approximated to a given plane, 
and their axes to parallelism. 



158 GRAVITATION 

CV. 

Discoveries of Newton and Kepler. 

The discovery of the three great laws of 
planetary motion by Kepler was a sublime dis- 
covery, as was also that of the law of gravita- 
tion by Newton, to account for the former. 
Newton conceived that all matter has the 
power to attract all other matter, and that this 
force of attraction decreases inversely as the 
square of the distance from the center of the 
earth. He established this law of gravitation, 
by comparing the magnitude of the devia- 
tion of the moon from a right line, caused by 
terrestrial gravitation, with the space through 
which a body falls, in a given time, at the 
surface of the earth. He also considered, at 
great length (" Principia," Book II., sections 
6 and 7), the effect that a resisting medium 
has on a falling body, and in his closing para- 
graph he says : " The resistance in every fluid 
is as the motion excited by the projectile in 
the fluid ; and cannot be less in the most sub- 
tle ether, in proportion to the density of that 
ether, than it is in air, water, and quicksilver, 
in proportion to the densities of those fluids." 



THE DETERMINING FORCE. 159 



CVI. 

Question of Interplanetary Eesistance Un- 
decided. 

It would seem from the number and the 
delicacy of Newton's experiments that he 
must have arrived at correct conclusions, but 
he did not fully decide whether there is any 
resistance in planetary space. For when 
bringing forward his theory of " The system 
of the World/' he says (" Principia," p. 513), 
" The celestial motions are scarcely retarded, 
by the little or no resistance of the space in 
which they are performed." It may be im- 
possible to decide this question without ex- 
tending the researches farther than Newton 
did, and determining what effect resistance 
has on a falling body that has an axial rota- 
tion ; for if the ethereal medium had the ef- 
fect only to retard the planets, their centrifu- 
gal force would be diminished, shortening 
their orbits, and possibly without affecting 
their periodic times. In this case, even if 
there were resistance, we should be unable to 
detect it* 



160 GRAVITATION 



CVIL 

Important Results of Experiment, and their 
Practical Application. 

In the case of the moon, it has been 
claimed that the resistance accelerates its 
mean motion. If Newton was correct in his 
conclusions, there is no subtle ether in the 
paths of the planets, whatever there may be 
near the sun, as their motions are not resisted ; 
or if any does exist, it does not retard the mo- 
tions of the planets. This is made evident by 
extending the researches of Newton to bodies 
falling through a resisting medium, these bod- 
ies having at the same time an axial rotation. 

The results of the following experiment are 
significant. Having imparted a rotatory mo- 
tion of a few thousands of revolutions per 
minute to a solid metallic ball a couple of 
inches in diameter, and then allowing it to 
fall through the resisting atmosphere a dis- 
tance of thirty-five feet, I found that it devi- 
ated more than three inches from a true per- 
pendicular. 1 

1 Some years since this experiment was explained to a 
United States Army officer of high rank, and although my 
conclusions were not accepted at the time, they were appro- 
priated and applied in a work on gunnery which the officer 
issued a few years later. 



THE DETERMINING FORCE. 161 

Although the axial rotation and deviation 
of the ball from a right line agrees with the 
axial rotation of the earth and its deviation 
from a rectilineal path, the deviation of the 
earth is not caused by any resistance in space, 
but by gravity ; yet, if the translating and 
rotating velocities of the earth could be main- 
tained in a resisting medium, it might sustain 
its orbital motion without the aid of any cen- 
tripetal force. However, the agreement is 
such that the query naturally arises, whether 
or not the increased centrifugal force existing 
in the outer limbs of the planets and the in- 
creased tendency of those linibs to move off 
on a tangent, over and above such tendency 
in the inferior limbs, has not something to do 
with their axial rotation. 

The curvilinear path of the falling ball 
shows that if the translating and rotating ve- 
locities were perpetuated, it would move in a 
very" small orbit without any centripetal force, 
simply through the influence of the resistance 
of the air acting unequally on the opposite 
equatorial sides of the rotating sphere, at 
right angles with its motion of translation. 

The compression of the air, caused by the 
rotation of the ball coming in contact with 
the air which the ball is falling against, 



162 GRAVITATION 

crowds the ball from a vertical line. But if 
the ball were a projectile, having a rotary mo- 
tion, as when thrown from a rifle, the motion 
of the rotation of the air caused by the rota- 
tion of the projectile would not coincide with 
the equatorial plane of the rotating projectile 
(as in the above case), but would drop back 
at an acute angle with that plane, and would 
thus act on the stern of the ball very much 
as the rudder acts on a ship, causing the ball 
to turn and drift away from the direction of 
the projectile force. The more the projec- 
tile is elongated, the more perceptible the 
drifting motion would be. Moreover, while 
the ball was passing upward from a horizontal 
line, the air would be crowding on one side, 
causing the ball for the time being to drift 
in one direction ; but when it was dropping 
downward from a horizontal line, the air 
would crowd on the other side, and cause a 
drifting motion in the opposite direction. 

Independent of the effect which the atmos- 
phere has on the rifle projectile, it is well 
known that the tendency of the rotation is to 
hold the equator of the ball in a given plane 
and to keep the axis of rotation constantly 
parallel to the position it had previously occu- 
pied, as is illustrated by the movement of the 
earth in its orbit. 



THE DETERMINING FORCE. 163 

This tendency was indicated by the be- 
havior of the projectiles used in the earlier 
bombardments of Charleston, in our late civil 



cvm. 

The Distances and Periodic Times of Plants 
and Comets Indicate the Absence of a Ke- 
sisting Medium. 

According to Newton's theory, if there is 
any subtle ether, the falling ball must be re- 
sisted, and the deviation of the rotating fall- 
ing ball demonstrates that if the motion of 
the planets were resisted, their masses, varia- 
tion in axial rotation, and the translating ve- 
locities in their orbits being so unequal, the 
magnitude of their orbits, and their periodic 
times, must be unequally diminished. 

Their periodic times would not then be as- 
signable by Kepler's third law, or by New- 
ton's law of gravitation. The distance be- 
tween the earth and the sun, and the periodic 
time of the earth, would be diminished, and 
the distance between the earth and the moon 
would be increased, as would be the periodic 
time of the moon. These results would be 
caused by the unequal dimensions and un- 
equal axial rotation of these bodies. On ac- 



164 GRAVITATION 

count of the decrease in the periodic times of 
Encke's and Fay's comets, Encke assumed 
that planetary space is pervaded by an ex- 
tremely rare medium. But, as it is demon- 
strated that the motion of the planets is not 
resisted, and the orbits of these comets are 
interplanetary, the decrease in their periodic 
times cannot be accounted for by that theory. 

Again, the unequal variation of their peri- 
odic times conflicts with the same theory. To 
account for this, it has been conjectured 
" that the resistance arises from collision with 
innumerable small bodies revolving about the 
sun." That these bodies exist in abundance 
is evident ; but the effect they may have on 
the periodic times of the comets can hardly 
be determined by experiment. 

There is another proof that no resisting 
medium peryacles the space in which the 
earth's orbit lies that, so far as I am aware, 
has not been noticed, viz., The existence of 
such a resisting medium would inevitably pro- 
duce a decided effect upon the earth's atmos- 
phere, causing it to be very unequally distrib- 
uted over the earth's surface — the greater 
portion following behind, so that were it illu- 
minated and visible to an outside observer, it 
would present an appearance somewhat like 
the tail of a comet. 



THE DETERMINING FORCE. 165 

CIX. 

Author's Conclusions Harmonize with Scrip- 
tural Eepresentations. 

As the density of matter depends upon the 
conditions determined by the force of gravi- 
tation, matter must have existed, prior to its 
condensation, in a gaseous or nebulous form. 
I believe that this view of the primitive condi- 
tion of matter harmonizes with the account 
of creation given by Moses in the Book of 
Genesis. From that we learn that the heavens 
and the earth had a material beginning. As 
in the first chapter of St. John we are told of 
the spiritual beginning, or the entrance of the 
Spirit into the world. Moses tells us that the 
matter of which the earth is composed " was 
without form," indicating that it was a very 
rare fluid, to us " a void," and that darkness 
was upon the deep, or abyss of celestial space, 
until the " Spirit of God moved (by the 
agency of gravitation) upon the face of the 
waters," or fluids, to condense them. " And 
there was light;" when the surface of the 
earth became refrigerated and dark, " God di- 
vided the light from the darkness," but the 
length of time intervening is not specified. 
" And God called the light day, and the dark- 



166 GRAVITATION 

ness he called night. And the evening and 
the morning were the first day," or period. 
It is well to note the words of St. Peter : 
" But, beloved, be not ignorant of this one 
thing, that one day is with the Lord as a 
thousand years, and a thousand years as one 
day." It was necessary that the fluid, or 
" waters which were under the firmament,' ' 
should be " divided from the waters which 
were above the firmament " in the formation 
of the solar system from nebulous matter. 
After the waters were thus divided, and the 
planets formed, " God called the firmament," 
or celestial space, " heaven." 

The primitive condensation would cause a 
high temperature. The waters were held in 
suspense until the surface refrigeration formed 
mountains and valleys as we are told : " There 
went up a mist from the earth and watered 
the whole face of the ground." When the 
surface temperature became sufficiently re- 
duced to allow the suspended fluids to be con- 
densed, " the waters under the heavens were 
gathered together into one place," the de- 
pressed portions of the earth, " and the dry 
land appeared." When the overhanging mist 
became condensed, " the lights were set," or 
became visible, " in the firmament of the 



THE DETERMINING FORCE. 167 

heavens, to give light upon the earth." The 
first verse of the first chapter of Genesis, in 
an introductory way, speaks of the creation of 
the heavens and the earth. The second, third, 
fourth, and fifth verses speak more particu- 
larly, of the creation of the earth. The sixth, 
seventh, and eighth relate to the creation of 
the solar system. The ninth to the thirteenth 
inclusive speak still further of the creation of 
the earth. The fourteenth to the eighteenth 
inclusive tell us of the earth and the appear- 
ance of the solar system, after the surround- 
ing mist, or waters, had been gathered to- 
gether into one place. The last cited verses 
determine the division of time into seasons 
and days and years as we have them now, ex- 
cept that the length of the day has decreased 
by a very small fraction, since the fourth day, 
or period, of creation, by the refrigeration, or 
very slight contraction of the earth which 
took place in the early period. 

CX. 

Space Originally Pervaded by Homogeneous 
Nebulous Matter. 

We are therefore led by revelation, as well 
as by science, to believe that the matter of 



168 GRAVITATION 

which the earth and planets were formed 
originally pervaded space in a homogeneous 
nebulous form. If the density of the solar 
system were estimated in accordance with this 
theory, a cubic mile of such matter, it is said, 
would weigh less than a cubic inch of our at- 
mosphere, and space thus occupied might well 
be called a " void." 

When the matter of the solar system was 
in a nebulous form, and the force which 
caused particle to attract particle was imparted 
to it, the planetary system, following nature's 
laws, took its form fitted for life. 

CXI. 
The Consummation. 

If the force of gravitation should be re- 
moved from the solar system, many prophecies 
in Holy Writ would be fulfilled. The sun 
would " become black," owing to expansion ; 
but the moon and the earth would be melted 
and " become as blood ; " " and the stars " 
or planets, by expansion, " would fall unto 
the earth, and the heavens depart as a scroll 
when it is rolled together." Rev. 6 : 12-14. 
Isaiah 34 : 4. 

Independent of translating forces, the ex- 



THE DETERMINING FORCE. 169 

pansion of matter in so many conflicting 
directions might tend to restore comparative 
rest. 

Again, if we look out into the starry heav- 
ens, the probability that the earth is to be 
burned up is confirmed. Astronomers have 
computed that more than fifteen hundred 
fixed stars have disappeared within the last 
three centuries. Some of these stars may 
have become dark and invisible by surface re- 
frigeration, as is the case with the earth. Oth- 
ers have given the most indisputable evidence 
of having been consumed. Their light has 
broken forth with such splendor that they 
could be seen by the naked eye, at noonday, 
and at night through a canopy of clouds. 
After the conflagration had been visible for a 
few months, the stars disappeared. 

May the Creator of the universe grant that 
we may be prepared for that hour, when our 
works shall be tried by fire. 




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